Multiple choice general knowledge math & puzzles

In one of the locker byomkesh finds a note saying “Catch Me If You Can”. I live at the door number given by the solution of this question “How many pairs of natural numbers is there the difference of whose square is 45”. Help byomkesh

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For natural numbers a > b > 0, the difference of squares is a² - b² = 45, which factors as (a-b)(a+b) = 45. The factor pairs of 45 are (1,45), (3,15), and (5,9). Each pair yields a valid solution for (a,b): (23,22), (9,6), and (7,2).

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