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80
A 80
A 80
Source:
May 25, 2007
inequalities
algebra
polynomial
Divisibility Theory
Problem Statement
Find all pairs of positive integers
m
,
n
≥
3
m, n \ge 3
m
,
n
≥
3
for which there exist infinitely many positive integers
a
a
a
such that
a
m
+
a
−
1
a
n
+
a
2
−
1
\frac{a^{m}+a-1}{a^{n}+a^{2}-1}
a
n
+
a
2
−
1
a
m
+
a
−
1
is itself an integer.
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