Given any positive integers c and e.

Any hints?

Thanks in advance!

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- Oct 14th 2012, 01:10 PMjsaetrumDeciding whether an integer c is an eth power in Z
Given any positive integers c and e.

Any hints?

Thanks in advance! - Oct 15th 2012, 12:19 AMchiroRe: Deciding whether an integer c is an eth power in Z
Hey jsaetrum.

Can you give an equation or relationship in mathematical form? - Oct 15th 2012, 02:00 AMjsaetrumRe: 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:

$\displaystyle c=m^e$

for any integer m

and thus satisfying the following:

$\displaystyle m^e \equiv 1\mod(c-1)$ - Oct 26th 2012, 03:32 AMSalahuddin559Re: 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