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what will be the remainder when 5^97 is ...

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

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`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`
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