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 reply to
re: Puzzle Answer by Larry)
It's ambiguous as to what is meant by "powers". In retrospect, application to the exponents does seem to make this a very high value for that component.
But the Wikipedia article on "Exponent" says
In mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n".[1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:[1]
Hence, the ambiguity.
Edited on September 24, 2023, 7:33 am
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Posted by Charlie
on 2023-09-24 07:27:17 |
re(2): Puzzle Answer
