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

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

To attain the answer $m + n = 4 p + 3$ it will be necessary to have the following numbers.
${m}^{2} + {n}^{2} = 16 {p}^{2} + 24 p + 1$