Question
What will be the remainder which 5382 + 53 is
divided by 54?Solution
(53)82 + 53 = 53[(53)81 + 1] Clearly (an + 1) is always divisible by (a + 1) which n is odd. So (53)81 + 1 is divisible by (53 + 1) 54, Thus remainder is zero.
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