JEE Main 2022 (Online) 28th July Morning ShiftQuestion 1
The remainder when $7^{2022}+3^{2022}$ is divided by $5$ is :
Binomial Theorem · Remainder and Divisibility
Solution
Concept. Reduce each base modulo $5$ and use a power that is $1$. Formulas used. (1) $2^4=16\equiv1$ and $3^4=81\equiv1\pmod5$Step 1 - First term. $7\equiv2$, and $2022=4\cdot505+2$. By (1), $7^{2022}\equiv2^2=4$. Step 2 - Second term. By (1), $3^{2022}\equiv3^2=9\equiv4$. Step 3 - Add. $4+4=8\equiv3\pmod5$. Answer: (C)