perplexus.info :: Numbers : Checking the quantity

Checking the quantity (Posted on 2023-09-23)

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.

No Solution Yet Submitted by Ady TZIDON

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Colloquial ambiguity

| Comment 7 of 8 |

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 non-US parts of the world) would say "two power four": again 4 is the power.

Posted by Larry on 2023-09-24 08:06:00

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