It is known that \(a + b + c = 5\) and \(ab + bc + ac = 5\). What are the possible values of \(a^2 + b^2 + c^2\)?
Find all the prime numbers \(p\) such that there exist natural numbers \(x\) and \(y\) for which \(p^x = y^3 + 1\).
Determine all prime numbers \(p\) such that \(5p+1\) is also prime.