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Remainder of a power when the base is 1 more or 1 less than a multiple of the divisor

This type of question, asked 6 times: 14 Jul 2023 S1, 25 Jul 2023 S1, 10 Sep 2024 S2, 13 Sep 2024 S3, 18 Sep 2024 S2, 26 Sep 2024 S1. All 6 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S1

    75
    What will be the remainder when (265)4081+9(265)^{4081} + 9 is divided by 266?

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  2. Question 2

    25 Jul 2023 S1

    59
    Find the remainder when 88+68^8 + 6 is divided by 7.

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  3. Question 3

    10 Sep 2024 S2

    68
    If (7777+77)(77^{77} + 77) is divided by 78, then the remainder will be:

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  4. Question 4

    13 Sep 2024 S3

    73
    Find the remainder: (1713−21)÷18(17^{13} - 21) \div 18

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  5. Question 5

    18 Sep 2024 S2

    65
    Find the remainder, if 1920019^{200} is divided by 20.

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  6. Question 6

    26 Sep 2024 S1

    61
    Find the remainder when 920+29^{20} + 2 is divided by 4.

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