p^a+q^b=r^c

How many distinct solutions of the equation above are there, subject to the following constraints:

p, q, & r distinct primes
a, b, & c distinct positive integers,
each more than one
None of the powers exceeds 1111.

Being impartial to the formal definition I understand the grounds for ambiguity, but must specify that my perception of the word power was not the exponent but the whole entity base, exponent and the resulting outcome.

Edited on September 25, 2023, 6:16 am

Posted by Ady TZIDON on 2023-09-25 05:36:34