Question

what will be the remainder when `5^97` is divided by `52`

Answer 1

`5^(97) = 5^96*5 = (5^4)^24*5 = (625)^24*5`
`:. 5^97/52 = ((625)^24*5)/52`
If we divide, `625` by `52`, then remainder is `1`.
`:.` Remainder when `(625)^24*5` is divided by `52 = 1^24*5 = 5`