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Is an expression in powers divisible by given numbers

This type of question, asked 2 times: 6 Apr 2023, 8 Apr 2023. All 2 questions below, oldest first.

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  1. Question 1

    6 Apr 2023

    152
    Among the statements: (S1): 20232022−199920222023^{2022}-1999^{2022} is divisible by 8. (S2): 13(13)n−11n−1313(13)^{n}- 11n - 13 is divisible by 144 for infinitely many n∈Nn \in N.

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  2. Question 2

    8 Apr 2023

    163
    25190−19190−8190+219025^{190}-19^{190}-8^{190}+2^{190} is divisible by

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