WHAT IS THE REMAINDER WHEN
alt="32^{37^{32} }" align="absmiddle" class="latex-formula"> IS DIVIDED BY 9?
1 answer:
Recall Euler's theorem: if
, then

where
is Euler's totient function.
We have
- in fact,
for any
since
and
share no common divisors - as well as
.
Now,

where the
are positive integer coefficients from the binomial expansion. By Euler's theorem,

so that

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