# Oh my! 100th powers!

**Computer Science**Level 5

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.