MathDB

n

is a positive integer which can be expressed in the form

n=a^{2}+b^{2}+c^{2}

, where

a, b, c

are positive integers, prove that for each positive integer

k

n^{2k}

can be expressed in the form

A^2 +B^2 +C^2

, where

A, B, C

are positive integers.

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