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GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 25

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Fermat's little theorem states that if $p$ is a prime number, then for any integer $a,$ the number $a^p – a$ is an integer multiple of $p.$ Here, $a = 60, p = 61.$ So, we get

$60^{61} - 60$ is an integral multiple of $61.$

$\implies 60^{61}$ divided by $61$ leaves a remainder of $60.$
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