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Kyrgyzstan Contests
Kyrgyzstan Regional Olympiad
2017 Kyrgyzstan Regional Olympiad
4
number theory
number theory
Source: kyrgyzstan regional
March 7, 2017
number theory
Problem Statement
Prove that for all n=3,4,5.... there excist odd x,y such
2
n
=
x
2
+
7
y
2
2^n=x^2 + 7y^2
2
n
=
x
2
+
7
y
2
.
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