# Oh my! 100th powers!

Let N be the number of positive integers m for which

$3^{100}\equiv2^{100} \pmod m$

Then N can be expressed as $2^k$

Find the value of $k$.

Details For those who don't know Mod notation :

$a\equiv b \pmod c$ if and only if "$a$" and "$b$" give the SAME remainder when divided by $c$.

And this information is enough to find the trick which makes the problem easy.

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