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.
In common terminology, for base^exponent, the word power sometimes means the exponent and sometimes the entire expression.
We say 81 is a perfect square and also a 4th power: 81 is the power.
But we read 2^4 as "two to the fourth power": 4 is the power.
Some English speakers (I think UK and possibly many nonUS parts of the world) would say "two power four": again 4 is the power.

Posted by Larry
on 20230924 08:06:00 