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2020 Caucasus Mathematical Olympiad
5
One more equation in positive integers
One more equation in positive integers
Source: 2020 Caucasus Mathematical Olympiad
March 16, 2020
algebra
Problem Statement
Find the number of pairs of positive integers
a
a
a
and
b
b
b
such that
a
≤
100
000
a\leq 100\,000
a
≤
100
000
,
b
≤
100
000
b\leq 100\,000
b
≤
100
000
, and
a
3
−
b
a
3
+
b
=
b
2
−
a
2
b
2
+
a
2
.
\frac{a^3-b}{a^3+b}=\frac{b^2-a^2}{b^2+a^2}.
a
3
+
b
a
3
−
b
=
b
2
+
a
2
b
2
−
a
2
.
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