{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:03:59Z","timestamp":1776841439905,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"233","license":[{"start":{"date-parts":[[2001,6,12]],"date-time":"2001-06-12T00:00:00Z","timestamp":992304000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p comma q comma r comma s\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p,q,r,s<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be polynomials with integer coefficients. This paper presents a fast method, using very little temporary storage, to find all small integers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis a comma b comma c comma d right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>b<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(a,b,c,d)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    satisfying\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p left-parenthesis a right-parenthesis plus q left-parenthesis b right-parenthesis equals r left-parenthesis c right-parenthesis plus s left-parenthesis d right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>b<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p(a)+q(b)=r(c)+s(d)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Numerical results include all small solutions to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a Superscript 4 Baseline plus b Superscript 4 Baseline plus c Superscript 4 Baseline equals d Superscript 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>c<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>d<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\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                    ; all small solutions to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a Superscript 4 Baseline plus b Superscript 4 Baseline equals c Superscript 4 Baseline plus d Superscript 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>b<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>c<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>d<\/mml:mi>\n                              <mml:mn>4<\/mml:mn>\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                    ; and the smallest positive integer that can be written in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"5\">\n                        <mml:semantics>\n                          <mml:mn>5<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">5<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ways as a sum of two coprime cubes.\n                  <\/p>","DOI":"10.1090\/s0025-5718-00-01219-9","type":"journal-article","created":{"date-parts":[[2005,7,11]],"date-time":"2005-07-11T17:02:26Z","timestamp":1121101346000},"page":"389-394","source":"Crossref","is-referenced-by-count":16,"title":["Enumerating solutions to \ud835\udc5d(\ud835\udc4e)+\ud835\udc5e(\ud835\udc4f)=\ud835\udc5f(\ud835\udc50)+\ud835\udc60(\ud835\udc51)"],"prefix":"10.1090","volume":"70","author":[{"given":"Daniel","family":"Bernstein","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,6,12]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/BF01937350","article-title":"Average-case results on Heapsort","volume":"27","author":"Carlsson, Svante","year":"1987","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"issue":"216","key":"2","doi-asserted-by":"publisher","first-page":"1755","DOI":"10.1090\/S0025-5718-96-00768-5","article-title":"Equal sums of four seventh powers","volume":"65","author":"Ekl, Randy L.","year":"1996","journal-title":"Math. 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