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Dutch IMO TST
2021 Dutch IMO TST
3
n | 4a^2 + 9b^2 -1
n | 4a^2 + 9b^2 -1
Source: 2021 Dutch IMO TST 2.3
December 28, 2021
number theory
divides
divisible
Problem Statement
Prove that for every positive integer
n
n
n
there are positive integers
a
a
a
and
b
b
b
exist with
n
∣
4
a
2
+
9
b
2
−
1
n | 4a^2 + 9b^2 -1
n
∣4
a
2
+
9
b
2
−
1
.
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