Calculate if a digital signature is valid
Basically RSA signatures work just like encryption but with the keys exchanged.
If somebody tells you $m^{sk}$ you can easily test if
$$
(m^{sk})^{pk} \equiv m\ (mod\ N)
$$
but you cannot calculate $m^{sk}$ yourself.

The problem/trick is the usual, exponentiation is easy but logarithm is hard.

(I like using $sk$/$pk$ for secret-/public-key rather than $d$/$e$ for decryption-/encryption-key as it makes more sense for signatures.)