The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair. (Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

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Let's analyze the difference between the numbers in each pair:

- 34 : 44 → Difference is 10 (44 - 34 = 10)
- 23 : 25 → Difference is 2 (25 - 23 = 2)
- 13 : 16 → Difference is 3 (16 - 13 = 3)
- 35 : 36 → Difference is 1 (36 - 35 = 1)

Now, let's check if these differences follow a mathematical pattern:
- For pairs (23, 25) and (13, 16), the differences (2 and 3) are both prime numbers.
- For pair (35, 36), the difference is 1, which is a perfect square.
- For pair (34, 44), the difference is 10, which is neither a prime number nor a perfect square.

Additionally, among the differences, only 10 does not fit the pattern of being a small prime or a perfect square, while the others do.

Therefore, the odd number pair is 34 : 44, as its difference does not match the pattern followed by the other pairs.

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