-2

i'am struggling to solve this problem can you help me please Let $p$ be a prime number such that there exists two positive integers $m,n$ s.t $$p^2=\frac{(m^2+n^2)}{2}$$

Prove that there exists a positive integer a such that :

$$2p-m-n=a^2 \text{ or } 2p-m-n=2a^2$$

Pingu
  • 49
ayoub adnane
  • 1
  • 1
  • 5
    Welcome to MSE! Take a [tour]. We are NOT Your Friendly Neighborhood Homework Answering Service, and this question--no effort shown on your part and not enough context, makes many of us salty. This question also goes against the MSE Guidelines. So edit , saying what you have tried, and the contest this question is from, Pls &thx – Mike Mar 29 '24 at 17:06
  • 2
    Also, this is false if you have $m = n = p$, as $a$ is not positive. – D S Mar 29 '24 at 17:47

0 Answers0