The remainder when ${\left((64{)}^{(64)}\right)}^{(64)}$ is divided by $7$ is equal to [JEE Main 2025, 7 Apr (Shift 1)]

Question

YESPYQ · Accepted Answer

Correct answer: b) $1$. ${64}^{64}=(63+1{)}^{64}=63{\lambda }_{1}+1$ ${({(64)}^{(64)})}^{(64)}=(63\lambda +1{)}^{64}=63{\lambda }_{2}+1$

The remainder when \({\left((64{)}^{(64)}\right)}^{(64)}\) is divided by \(7\) is equal to [JEE Main 2025, 7 Apr (Shift …