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Fermat's little theorem: a^(p-1) leaves remainder 1 on division by prime p

This type of question, asked 3 times: CDS 2 2016, CDS 1 2017, CDS 1 2025. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    15
    What is the remainder when 21002^{100} is divided by 101 ?

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  2. Question 2

    CDS 1 2017

    48
    (Np−1−1)(N^{p-1} - 1) is a multiple of pp, if NN is prime to pp and pp is a

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  3. Question 3

    CDS 1 2025

    78
    What is the remainder when 21012^{101} is divided by 101 ?

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  4. Question 4

    CDS 1 2025

    47
    What is the remainder when 2p−12^p - 1 is divided by p, where p>5p > 5 is a prime number ?

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