MathDB

Let a and b be non-negative integers such that

ab \ge c^{2}

where

c

is an integer. Prove that there is a positive integer n and integers

x_{1}

x_{2}

\cdots

x_{n}

y_{1}

y_{2}

\cdots

y_{n}

such that

{x_{1}}^{2}+\cdots+{x_{n}}^{2}=a,\;{y_{1}}^{2}+\cdots+{y_{n}}^{2}=b,\; x_{1}y_{1}+\cdots+x_{n}y_{n}=c

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