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Remainder when one large power is divided by a number

This type of question, asked 11 times: 2021 Paper 4, 2021 Paper 7, 14 Jun 2022, 26 Jun 2022, 25 Jan 2023, 31 Jan 2023, 13 Apr 2023, 29 Jan 2024, 9 Apr 2024, 29 Jan 2025, 7 Apr 2025. All 12 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    84
    If the remainder when xx is divided by 4 is 3 , then the remainder when (2020+x)2022(2020 +x)^{2022} is divided by 8 is

  2. Question 2

    2021 Paper 7

    90
    If (2021)3762(2021)^{3762} is divided by 17, then the remainder is

  3. Question 3

    14 Jun 2022

    62
    The remainder when 320223^{2022} is divided by 5 is

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  4. Question 4

    26 Jun 2022

    65
    The remainder when (2021)2023(2021)^{2023} is divided by 7 is:

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  5. Question 5

    25 Jan 2023

    172
    The remainder when (2023)2023(2023)^{2023} is divided by 35 is

  6. Question 6

    31 Jan 2023

    90
    The remainder on dividing 5995^{99} by 11 is:

  7. Question 7

    13 Apr 2023

    75
    Fractional part of the number 4202215\frac{4^{2022}}{15} is equal to

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  8. Question 8

    13 Apr 2023

    180
    The remainder, when 71037^{103} is divided by 17 is

  9. Question 9

    29 Jan 2024

    178
    Remainder when 64323264^{32^{32}} is divided by 9 is equal to

  10. Question 10

    9 Apr 2024

    85
    The remainder when 4282024428^{2024} is divided by 21 is

  11. Question 11

    29 Jan 2025

    142
    The remainder, when 71037^{103} is divided by 23 , is equal to:

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  12. Question 12

    7 Apr 2025

    54
    The remainder when ((64)(64))(64)\left( (64)^{(64)} \right)^{(64)} is divided by 7 is equal to.

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