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Remainder of a^(odd power) plus or minus c divided by a + 1

The same question, asked 3 times: 14 Jul 2023 S1*, 10 Sep 2024 S2*, 13 Sep 2024 S3. Every wording 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

    10 Sep 2024 S2

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

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  3. Question 3

    13 Sep 2024 S3

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

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