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NOTE: I am beginner in proofs.

  • Even number form = 2a
  • Odd number form = 2b + 1

Assume initially both “m” and “n” are odd, hence we can write:

  • m = 2a+ 1
  • n = 2b+1

Now m X n = (2a + 1) X (2b + 1) = 2a2b + 2a + 2b + 1, which is an odd number.

Hence we can say that, when two odd numbers(m, n) are multiplied together, the result(mn) is always an odd number. But it is given in the question that result(mn) is even hence “m” is even or “n” is even.

 

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