# Deciding whether an integer c is an eth power in Z

• October 14th 2012, 01:10 PM
jsaetrum
Deciding whether an integer c is an eth power in Z
Given any positive integers c and e.

Any hints?

• October 15th 2012, 12:19 AM
chiro
Re: Deciding whether an integer c is an eth power in Z
Hey jsaetrum.

Can you give an equation or relationship in mathematical form?
• October 15th 2012, 02:00 AM
jsaetrum
Re: Deciding whether an integer c is an eth power in Z
I tried to express this as a congruence (inverse modulo), i'm not sure it is right, but it seems to be:

$c=m^e$

for any integer m

and thus satisfying the following:

$m^e \equiv 1\mod(c-1)$
• October 26th 2012, 03:32 AM
Salahuddin559
Re: Deciding whether an integer c is an eth power in Z
I can give you a computer procedure (algorithm) to solve it. It best works out using divisions. (If needed, take "large integers package" like BigInteger from Java or something). Keep dividing c by m, until you get a fraction, or c, or a positive number less than c. Of these outcomes, getting c means, it is a power, other outcomes prove that it is not.

Salahuddin
Maths online