{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T09:58:35Z","timestamp":1776765515689,"version":"3.51.2"},"reference-count":4,"publisher":"American Mathematical Society (AMS)","issue":"216","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, the method used to find the smallest, nontrivial, positive integer solution of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a 1 Superscript 7 Baseline plus a 2 Superscript 7 Baseline plus a 3 Superscript 7 Baseline plus a 4 Superscript 7 Baseline equals b 1 Superscript 7 Baseline plus b 2 Superscript 7 Baseline plus b 3 Superscript 7 Baseline plus b 4 Superscript 7\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msubsup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msubsup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">a_1^7+a_2^7+a_3^7+a_4^7=b_1^7+b_2^7+b_3^7+b_4^7<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is discussed. The solution is\n                    <disp-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"149 Superscript 7 Baseline plus 123 Superscript 7 Baseline plus 14 Superscript 7 Baseline plus 10 Superscript 7 Baseline equals 146 Superscript 7 Baseline plus 129 Superscript 7 Baseline plus 90 Superscript 7 Baseline plus 15 Superscript 7 Baseline period\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mn>149<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>123<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>14<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>146<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>129<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>90<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>15<\/mml:mn>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>.<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\begin{equation*} 149^7+123^7+14^7+10^7= 146^7+129^7+90^7+15^7.\\end{equation*}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/disp-formula>\n                    Factors enabling this discovery are advances in computing power, available workstation memory, and the appropriate choice of optimized algorithms.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00768-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"1755-1756","source":"Crossref","is-referenced-by-count":5,"title":["Equal sums of four seventh powers"],"prefix":"10.1090","volume":"65","author":[{"given":"Randy","family":"Ekl","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","unstructured":"[1] Richard K. Guy, Unsolved Problems in Number Theory, Second Edition, Springer-Verlag, New York, 1994."},{"key":"2","series-title":"Computer Software Engineering Series","volume-title":"Fundamentals of data structures","author":"Horowitz, Ellis","year":"1976"},{"key":"3","isbn-type":"print","volume-title":"An introduction to the theory of numbers","author":"Hardy, G. H.","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0198531702","edition":"5"},{"key":"4","doi-asserted-by":"publisher","first-page":"446","DOI":"10.2307\/2003249","article-title":"A survey of equal sums of like powers","volume":"21","author":"Lander, L. J.","year":"1967","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00768-5\/S0025-5718-96-00768-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00768-5\/S0025-5718-96-00768-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:17:53Z","timestamp":1776719873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00768-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":4,"journal-issue":{"issue":"216","published-print":{"date-parts":[[1996,10]]}},"alternative-id":["S0025-5718-96-00768-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00768-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}