If $m^{2} + n^{2} = 10 p^{2} + 10 p + 1$ $m^2+n^2=10p^2+10p+1$ , where $m$ $m$ and $n$ $n$ are positive integers and $p$ $p$ is a prime number, what is $m + n$ $m+n$ in terms of $p$ $p$ ?

Question

The answer is $4 p + 3$ $4p+3$ but I'm not sure how to get there.

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Answer 1 · 2016-08-30T23:09:01

Check the numbers, please.

To attain the answer $m + n = 4 p + 3$ $m+n=4p+3$ it will be necessary to have the following numbers.

$m^{2} + n^{2} = 16 p^{2} + 24 p + 1$ $m^2+n^2=16p^2+24p+1$