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2017 Turkey Team Selection Test
6
Turkey TST Number Theory Problem
Turkey TST Number Theory Problem
Source: Turkey Team Selection Test 2017 P6
April 6, 2017
number theory
Problem Statement
Prove that no pair of different positive integers
(
m
,
n
)
(m, n)
(
m
,
n
)
exist, such that
4
m
2
n
2
−
1
(
m
2
−
n
2
)
2
\frac{4m^{2}n^{2}-1}{(m^{2}-n^2)^{2}}
(
m
2
−
n
2
)
2
4
m
2
n
2
−
1
is an integer.
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