If prime p divides a^2+b^2, b^2+c^2, does p divide...?

[karan]

If p is a prime number and p divides (a^2 + b^2) and (b^2 + c^2) both then, Is p divides (a^2 + c^2) or (a^2 - c^2) or a^2 or b^2

 

[Denis]

To start, have a looksee at (1^2 + 3^2) / 2 and (3^2 + 5^2) / 2 : don't forget 2 is a prime number.