Name the triple (a, b, c) of positive integres exist such that a,

Question

b, and c are prime and a squared and b squared = c?

Answer 1

There are an infinite number of such triples, such as
(3, 4, 5); (5, 12, 13); (7, 24, 25) and multiples thereof.

According to Fermat's conjecture, which was finally proven in 1995 after over 200 years, it only works when adding squares. There are no such integer triples for other powers.