Let
p
,
q
,
r
,
s
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
)
(a,b,c,d)
satisfying
p
(
a
)
+
q
(
b
)
=
r
(
c
)
+
s
(
d
)
p(a)+q(b)=r(c)+s(d)
. Numerical results include all small solutions to
a
4
+
b
4
+
c
4
=
d
4
a^4+b^4+c^4=d^4
; all small solutions to
a
4
+
b
4
=
c
4
+
d
4
a^4+b^4=c^4+d^4
; and the smallest positive integer that can be written in
5
5
ways as a sum of two coprime cubes.