Given any positive integers c and e.
Any hints?
Thanks in advance!
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:
$\displaystyle m^e \equiv 1\mod(c-1)$
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