If 17^241≡R(mod 13), then value of R is :

Compute $17^{241}\pmod{13}$.

$17\equiv 4 \pmod{13}$

So $17^{241}\equiv 4^{241}\pmod{13}$.

Since $13$ is prime, $\phi(13)=12$.

$4^{12}\equiv 1 \pmod{13}$

$241\equiv 1 \pmod{12}$

Hence

$4^{241}\equiv 4^{1}\equiv 4 \pmod{13}$

final answer: $4$