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Number of pairs of natural numbers whose squares differ by k

The same question, asked 2 times: CDS 1 2019*, CDS 2 2024. Every wording below, oldest first.

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  1. Question 1

    CDS 1 2019

    90
    How many pairs of natural numbers are there such that the difference of their squares is 35 ?

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  2. Question 2

    CDS 2 2024

    2
    The difference of the square of two natural numbers mm and nn (m>n)(m > n) is 72. How many pairs of natural numbers will satisfy ?

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