Odd number pair: n squared paired with (n + 1) squared

The same question, asked 2 times: 17 Jul 2023 S3*, 19 Sep 2024 S2. Every wording below, oldest first.

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Question 1
17 Jul 2023 S3
13 $The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs, except one. Find that odd number-pair. (NOTE: The relation should be found without breaking down the numbers into its constituent digits)$
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Question 2
19 Sep 2024 S2
16 $The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs, except one. Find that odd number-pair. (NOTE: The relation should be found without breaking down the numbers into its constituent digits)$
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Question 1