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Powers of three
Powers of three
Source: 2015 BAMO-12 #3
February 22, 2016
algebra
Diophantine Equations
Problem Statement
Let
k
k
k
be a positive integer. Prove that there exist integers
x
x
x
and
y
y
y
, neither of which is divisible by
3
3
3
, such that
x
2
+
2
y
2
=
3
k
x^2+2y^2 = 3^k
x
2
+
2
y
2
=
3
k
.
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