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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