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Count n in a range for which a^n + b^n (or a^n - a) is a multiple of a number

This type of question, asked 2 times: 2021 Paper 4, 15 Apr 2023. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    88
    The total number of two digit numbers ' nn ', such that 3n+7n3^{n}+7^{n} is a multiple of 10 , is

  2. Question 2

    15 Apr 2023

    86
    The number of elements in the set {n∈N:10≤n≤100\left\{ n \in\mathbb{N}:10 \leq n \leq 100 \right. and 3n−33^{n}- 3 is a multiple of 7}\} is