## Enumerating solutions to $p(a)+q(b)=r(c)+s(d)$

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- by Daniel J. Bernstein;
- Math. Comp.
**70**(2001), 389-394 - DOI: https://doi.org/10.1090/S0025-5718-00-01219-9
- Published electronically: June 12, 2000

## Abstract:

Let $p,q,r,s$ be polynomials with integer coefficients. This paper presents a fast method, using very little temporary storage, to find all small integers $(a,b,c,d)$ satisfying $p(a)+q(b)=r(c)+s(d)$. Numerical results include all small solutions to $a^4+b^4+c^4=d^4$; all small solutions to $a^4+b^4=c^4+d^4$; and the smallest positive integer that can be written in $5$ ways as a sum of two coprime cubes.## References

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## Bibliographic Information

**Daniel J. Bernstein**- Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249) The University of Illinois at Chicago, Chicago, IL 60607β7045
- Email: djb@pobox.com
- Received by editor(s): July 10, 1998
- Received by editor(s) in revised form: January 4, 1999
- Published electronically: June 12, 2000
- Additional Notes: The author was supported by the National Science Foundation under grant DMSβ9600083.
- © Copyright 2000 D. J. Bernstein
- Journal: Math. Comp.
**70**(2001), 389-394 - MSC (2000): Primary 11Y50; Secondary 11D25, 11D41, 11P05, 11Y16
- DOI: https://doi.org/10.1090/S0025-5718-00-01219-9
- MathSciNet review: 1709145