2021/111) For which primes p, 7p+4 is a perfect square?

 7p + 4 is a perfect square say $m^2$

so $7p = m^2 -4 = (m+2)(m-2)$

now there are 2 cases

1. p is 2 which gives 7p + 4 = 18 which is not a perfect square

so

2. p is odd

so 7p is odd and  $m^2 -4$ is odd

so m+2 and m-2 are co-primes as they differ by 4

so m+2 = 7, m-2 = p gives p = 3 which is prime and m = 5

or m+2 = p and m-2 = 7 giving m = 9 and p =11 which is a prime

so p = 3 or 11