{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:33:27Z","timestamp":1763390007361,"version":"3.45.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10998-025-00670-0","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T03:28:23Z","timestamp":1753154903000},"page":"546-567","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the representation of an integer in Ostrowski and recurrence numeration systems"],"prefix":"10.1007","volume":"91","author":[{"given":"Mohit","family":"Mittal","sequence":"first","affiliation":[]},{"given":"Divyum","family":"Sharma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"670_CR1","unstructured":"H.G. Senge, E.G. Straus, $${\\rm PV}$$-numbers and sets of multiplicity. In: Proceedings of the Washington State University Conference on Number Theory (Washington State Univ., Pullman, Wash., 1971), pp. 55\u201367. Dept. Math., Washington State Univ., Pullman, Wash., WA (1971)"},{"key":"670_CR2","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF02018464","volume":"3","author":"HG Senge","year":"1973","unstructured":"H.G. Senge, E.G. Straus, $${\\rm PV}$$-numbers and sets of multiplicity. Period. Math. Hungar. 3, 93\u2013100 (1973)","journal-title":"Period. Math. Hungar."},{"key":"670_CR3","first-page":"63","volume":"319","author":"CL Stewart","year":"1980","unstructured":"C.L. Stewart, On the representation of an integer in two different bases. J. Reine Angew. Math. 319, 63\u201372 (1980)","journal-title":"J. Reine Angew. Math."},{"issue":"1","key":"670_CR4","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s40316-013-0002-y","volume":"37","author":"Y Bugeaud","year":"2013","unstructured":"Y. Bugeaud, M. Cipu, M. Mignotte, On the representation of Fibonacci and Lucas numbers in an integer base. Ann. Math. Qu\u00e9. 37(1), 31\u201343 (2013)","journal-title":"Ann. Math. Qu\u00e9."},{"issue":"3","key":"670_CR5","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/0022-314X(90)90121-7","volume":"35","author":"HP Schlickewei","year":"1990","unstructured":"H.P. Schlickewei, Linear equations in integers with bounded sum of digits. J. Number Theory 35(3), 335\u2013344 (1990). https:\/\/doi.org\/10.1016\/0022-314X(90)90121-7","journal-title":"J. Number Theory"},{"key":"670_CR6","doi-asserted-by":"publisher","unstructured":"J.J. Bravo, F. Luca, On the Diophantine equation $$F_n+F_m=2^a$$. Quaest. Math. 39(3), 391\u2013400 (2016) https:\/\/doi.org\/10.2989\/16073606.2015.1070377","DOI":"10.2989\/16073606.2015.1070377"},{"issue":"A99","key":"670_CR7","first-page":"1","volume":"18","author":"KC Chim","year":"2018","unstructured":"K.C. Chim, V. Ziegler, On Diophantine equations involving sums of Fibonacci numbers and powers of 2. Integers 18(A99), 1\u201330 (2018)","journal-title":"Integers"},{"issue":"1\u20132","key":"670_CR8","doi-asserted-by":"publisher","first-page":"157","DOI":"10.5486\/pmd.2021.8833","volume":"98","author":"I Vukusic","year":"2021","unstructured":"I. Vukusic, V. Ziegler, On sums of Fibonacci numbers with few binary digits. Publ. Math. Debrecen 98(1\u20132), 157\u2013181 (2021). https:\/\/doi.org\/10.5486\/pmd.2021.8833","journal-title":"Publ. Math. Debrecen"},{"issue":"2","key":"670_CR9","doi-asserted-by":"publisher","first-page":"139","DOI":"10.4064\/aa180427-13-11","volume":"190","author":"V Ziegler","year":"2019","unstructured":"V. Ziegler, Effective results for linear equations in members of two recurrence sequences. Acta Arith 190(2), 139\u2013169 (2019). https:\/\/doi.org\/10.4064\/aa180427-13-11","journal-title":"Acta Arith"},{"key":"670_CR10","doi-asserted-by":"publisher","unstructured":"D. Sharma, On the representation of an imaginary quadratic integer in two different bases. Publ. Math. Debrecen (accepted) (2024). Preprint at https:\/\/doi.org\/10.48550\/arXiv.2311.17348","DOI":"10.48550\/arXiv.2311.17348"},{"issue":"1\u20132","key":"670_CR11","doi-asserted-by":"publisher","first-page":"145","DOI":"10.5486\/pmd.1993.1317","volume":"42","author":"A Peth\u0151","year":"1993","unstructured":"A. Peth\u0151, R.F. Tichy, $$S$$-unit equations, linear recurrences and digit expansions. Publ. Math. Debrecen 42(1\u20132), 145\u2013154 (1993). https:\/\/doi.org\/10.5486\/pmd.1993.1317","journal-title":"Publ. Math. Debrecen"},{"issue":"1\u20132","key":"670_CR12","doi-asserted-by":"publisher","first-page":"181","DOI":"10.5486\/PMD.2017.7562","volume":"90","author":"C Bert\u00f3k","year":"2017","unstructured":"C. Bert\u00f3k, L. Hajdu, F. Luca, D. Sharma, On the number of non-zero digits of integers in multi-base representations. Publ. Math. Debrecen 90(1\u20132), 181\u2013194 (2017)","journal-title":"Publ. Math. Debrecen"},{"key":"670_CR13","doi-asserted-by":"crossref","unstructured":"J.-H. Evertse, K. Gy\u0151ry, C.L. Stewart, R. Tijdeman, $$S$$-unit equations and their applications. In: New Advances in Transcendence Theory (Durham, 1986), pp. 110\u2013174. Cambridge Univ. Press, Cambridge (1988)","DOI":"10.1017\/CBO9780511897184.010"},{"issue":"4","key":"670_CR14","doi-asserted-by":"publisher","first-page":"389","DOI":"10.2989\/16073600009485986","volume":"23","author":"F Luca","year":"2000","unstructured":"F. Luca, Distinct digits in base $$b$$ expansions of linear recurrence sequences. Quaest. Math. 23(4), 389\u2013404 (2000). https:\/\/doi.org\/10.2989\/16073600009485986","journal-title":"Quaest. Math."},{"issue":"4","key":"670_CR15","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/S0195-6698(88)80061-1","volume":"9","author":"M Mignotte","year":"1988","unstructured":"M. Mignotte, Sur les entiers qui s\u2019\u00e9crivent simplement en diff\u00e9rentes bases. European J. Combin. 9(4), 307\u2013316 (1988). https:\/\/doi.org\/10.1016\/S0195-6698(88)80061-1","journal-title":"European J. Combin."},{"key":"670_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-023-2478-8","author":"L Spiegelhofer","year":"2023","unstructured":"L. Spiegelhofer, Collisions of digit sums in bases 2 and 3. Isr. J. Math. (2023). https:\/\/doi.org\/10.1007\/s11856-023-2478-8","journal-title":"Isr. J. Math."},{"issue":"1","key":"670_CR17","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF02940581","volume":"1","author":"A Ostrowski","year":"1922","unstructured":"A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximationen. Abh. Math. Sem. Univ. Hamburg 1(1), 77\u201398 (1922). https:\/\/doi.org\/10.1007\/BF02940581","journal-title":"Abh. Math. Sem. Univ. Hamburg"},{"key":"670_CR18","doi-asserted-by":"crossref","unstructured":"J.-P. Allouche, J. Shallit, Automatic Sequences. Cambridge University Press, Cambridge (2003). Theory, applications, generalizations","DOI":"10.1017\/CBO9780511546563"},{"key":"670_CR19","first-page":"179","volume":"41","author":"E Zeckendorf","year":"1972","unstructured":"E. Zeckendorf, Repr\u00e9sentation des nombres naturels par une somme de nombres de fibonacci ou de nombres de lucas. Bull. Soc. Roy. Sci. Li\u00e8ge 41, 179\u2013182 (1972)","journal-title":"Bull. Soc. Roy. Sci. Li\u00e8ge"},{"key":"670_CR20","doi-asserted-by":"crossref","unstructured":"V. Berth\u00e9, Autour du syst\u00e8me de num\u00e9ration d\u2019Ostrowski. vol. 8 (2), pp. 209\u2013239 (2001). Journ\u00e9es Montoises d\u2019Informatique Th\u00e9orique (Marne-la-Vall\u00e9e, 2000)","DOI":"10.36045\/bbms\/1102714170"},{"key":"670_CR21","first-page":"133","volume":"24","author":"G Barat","year":"2004","unstructured":"G. Barat, P. Liardet, Dynamical systems originated in the Ostrowski alpha-expansion. Ann. Univ. Sci. Budapest. Sect. Comput. 24, 133\u2013184 (2004)","journal-title":"Ann. Univ. Sci. Budapest. Sect. Comput."},{"issue":"5","key":"670_CR22","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1142\/S1793042122500506","volume":"18","author":"M Amri","year":"2022","unstructured":"M. Amri, L. Spiegelhofer, J. Thuswaldner, R\u00e9partition jointe dans les classes de r\u00e9sidus de la somme des chiffres pour deux repr\u00e9sentations d\u2019Ostrowski. Int. J. Number Theory 18(5), 955\u2013976 (2022)","journal-title":"Int. J. Number Theory"},{"key":"670_CR23","doi-asserted-by":"publisher","first-page":"401","DOI":"10.4064\/aa-20-4-401-416","volume":"20","author":"J B\u00e9sineau","year":"1972","unstructured":"J. B\u00e9sineau, Ind\u00e9pendance statistique d\u2019ensembles li\u00e9s \u00e0 la fonction \u201csomme des chiffres\u2019\u2019. Acta Arith 20, 401\u2013416 (1972)","journal-title":"Acta Arith"},{"issue":"1","key":"670_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5802\/aif.814","volume":"31","author":"J Coquet","year":"1981","unstructured":"J. Coquet, G. Rhin, P. Toffin, Repr\u00e9sentations des entiers naturels et ind\u00e9pendance statistique. II. Ann. Inst. Fourier (Grenoble) 31(1), 1\u201315 (1981)","journal-title":"II. Ann. Inst. Fourier (Grenoble)"},{"key":"670_CR25","doi-asserted-by":"crossref","unstructured":"A.O. Gel\u2019fond, Sur les nombres qui ont des propri\u00e9t\u00e9s additives et multiplicatives donn\u00e9es. Acta Arith 13, 259\u2013265 (1968)","DOI":"10.4064\/aa-13-3-259-265"},{"issue":"2","key":"670_CR26","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1006\/jnth.1998.2327","volume":"74","author":"D-H Kim","year":"1999","unstructured":"D.-H. Kim, On the joint distribution of $$q$$-additive functions in residue classes. J. Number Theory 74(2), 307\u2013336 (1999)","journal-title":"J. Number Theory"},{"issue":"2","key":"670_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2478\/udt-2019-0010","volume":"14","author":"D Sharma","year":"2019","unstructured":"D. Sharma, Joint distribution in residue classes of the base-$$q$$ and Ostrowski digital sums. Unif. Distrib. Theory 14(2), 1\u201326 (2019)","journal-title":"Unif. Distrib. Theory"},{"issue":"2","key":"670_CR28","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0022-314X(89)90011-5","volume":"33","author":"A Peth\u0151","year":"1989","unstructured":"A. Peth\u0151, R.F. Tichy, On digit expansions with respect to linear recurrences. J. Number Theory 33(2), 243\u2013256 (1989). https:\/\/doi.org\/10.1016\/0022-314X(89)90011-5","journal-title":"J. Number Theory"},{"key":"670_CR29","unstructured":"A. Peth\u0151, Perfect powers in second order recurrences. In: Topics in Classical Number Theory, Vol. I, II (Budapest, 1981). Colloq. Math. Soc. J\u00e1nos Bolyai, vol. 34, pp. 1217\u20131227. North-Holland, Amsterdam (1984)"},{"issue":"203","key":"670_CR30","doi-asserted-by":"publisher","first-page":"351","DOI":"10.2307\/2152958","volume":"61","author":"HW Lenstra Jr","year":"1993","unstructured":"H.W. Lenstra Jr., J.O. Shallit, Continued fractions and linear recurrences. Math. Comp. 61(203), 351\u2013354 (1993). https:\/\/doi.org\/10.2307\/2152958","journal-title":"Math. Comp."},{"key":"670_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511566042","volume-title":"Exponential Diophantine Equations","author":"TN Shorey","year":"1986","unstructured":"T.N. Shorey, R. Tijdeman, Exponential Diophantine Equations (Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1986)"},{"key":"670_CR32","unstructured":"M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 326. Springer-Verlag, Berlin (2000). Transcendence properties of the exponential function in several variables"},{"key":"670_CR33","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.jnt.2017.07.016","volume":"183","author":"KC Chim","year":"2018","unstructured":"K.C. Chim, I. Pink, V. Ziegler, On a variant of Pillai\u2019s problem II. J. Number Theory 183, 269\u2013290 (2018). https:\/\/doi.org\/10.1016\/j.jnt.2017.07.016","journal-title":"J. Number Theory"},{"issue":"4","key":"670_CR34","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1070\/im1998v062n04ABEH000190","volume":"62","author":"EM Matveev","year":"1998","unstructured":"E.M. Matveev, An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. Izv. Ross. Akad. Nauk Ser. Mat. 62(4), 81\u2013136 (1998). https:\/\/doi.org\/10.1070\/im1998v062n04ABEH000190","journal-title":"Izv. Ross. Akad. Nauk Ser. Mat."},{"key":"670_CR35","doi-asserted-by":"publisher","unstructured":"E.M. Matveev, An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II. Izv. Ross. Akad. Nauk Ser. Mat. 64(6), 125\u2013180 (2000) https:\/\/doi.org\/10.1070\/IM2000v064n06ABEH000314","DOI":"10.1070\/IM2000v064n06ABEH000314"},{"issue":"176","key":"670_CR36","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1090\/S0025-5718-1986-0856715-5","volume":"47","author":"A Peth\u0151","year":"1986","unstructured":"A. Peth\u0151, B.M.M. de Weger, Products of prime powers in binary recurrence sequences part i: The hyperbolic case, with an application to the generalized ramanujan-nagell equation. Math. Comput. 47(176), 713\u2013727 (1986). https:\/\/doi.org\/10.1090\/S0025-5718-1986-0856715-5","journal-title":"Math. Comput."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00670-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-025-00670-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00670-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:30:51Z","timestamp":1763389851000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-025-00670-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,22]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["670"],"URL":"https:\/\/doi.org\/10.1007\/s10998-025-00670-0","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2025,7,22]]},"assertion":[{"value":"3 March 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}