{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:55:34Z","timestamp":1776768934496,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"223","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    This paper reports on new results for the equation\n                    <disp-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"sigma-summation Underscript i equals 1 Overscript m Endscripts a Subscript i Superscript k Baseline equals sigma-summation Underscript j equals 1 Overscript n Endscripts b Subscript j Superscript k Baseline comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:munderover>\n                              <mml:mo>\n                                \u2211\n                                \n                              <\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>i<\/mml:mi>\n                                <mml:mo>=<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>m<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:munderover>\n                            <mml:msubsup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>i<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>k<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:munderover>\n                              <mml:mo>\n                                \u2211\n                                \n                              <\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>j<\/mml:mi>\n                                <mml:mo>=<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:munderover>\n                            <mml:msubsup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>j<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>k<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\begin{equation*}\\sum _{i=1}^{m} a_{i}^{k}=\\sum _{j=1}^{n} b_{j}^{k},\\end{equation*}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/disp-formula>\n                    i.e., equal sums of like powers. Since the 1967 Lander, Parkin and Selfridge survey paper [\n                    <italic>A Survey of Equal Sums of Like Powers<\/italic>\n                    , Mathematics of Computation\n                    <bold>21<\/bold>\n                    (1967), 446\u2013459], few other numeric results have been published (see Elkies [\n                    <italic>\n                      On\n                      <inline-formula content-type=\"math\/mathml\">\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A Superscript 4 Baseline plus upper B Superscript 4 Baseline plus upper C Superscript 4 Baseline equals upper D Superscript 4\">\n                          <mml:semantics>\n                            <mml:mrow>\n                              <mml:msup>\n                                <mml:mi>A<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mn>4<\/mml:mn>\n                                <\/mml:mrow>\n                              <\/mml:msup>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>B<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mn>4<\/mml:mn>\n                                <\/mml:mrow>\n                              <\/mml:msup>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mn>4<\/mml:mn>\n                                <\/mml:mrow>\n                              <\/mml:msup>\n                              <mml:mo>=<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>D<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mn>4<\/mml:mn>\n                                <\/mml:mrow>\n                              <\/mml:msup>\n                            <\/mml:mrow>\n                            <mml:annotation encoding=\"application\/x-tex\">A^{4}+B^{4}+C^{4} = D^{4}<\/mml:annotation>\n                          <\/mml:semantics>\n                        <\/mml:math>\n                      <\/inline-formula>\n                    <\/italic>\n                    , Mathematics of Computation\n                    <bold>51<\/bold>\n                    (1988), 825-835] and Ekl [\n                    <italic>Equal Sums of Four Seventh Powers<\/italic>\n                    , Mathematics of Computation\n                    <bold>65<\/bold>\n                    (1996), 1755-1756]). The present paper reports on several new smallest primitive solutions. Further, search limits have been extended in many cases, and tables of solutions are presented. Additionally, new solutions to the same class of problems in\n                    <italic>distinct<\/italic>\n                    integers have been discovered.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00979-x","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1309-1315","source":"Crossref","is-referenced-by-count":11,"title":["New results in equal sums of like powers"],"prefix":"10.1090","volume":"67","author":[{"given":"Randy","family":"Ekl","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","series-title":"Problem Books in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3585-4","volume-title":"Unsolved problems in number theory","author":"Guy, Richard K.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387942890","edition":"2"},{"key":"2","isbn-type":"print","volume-title":"An introduction to the theory of numbers","author":"Hardy, G. 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