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Let $n$ be a natural number.

Which of the following statements imply $5 | \gcd(2^n-3,3^n-2)$?

Select ALL that apply.

$5|n$.

$5|2^n-3$.

$n\equiv 1 \ \mathrm{mod } \ 4$.

$n\equiv 3 \ \mathrm{mod} \ 4$.