Is the sum of two odd numbers always odd?

charmbraqdy

charmbraqdy

Answered question

2022-11-17

Is the sum of two odd numbers always odd?

Answer & Explanation

Cseszteq5j

Cseszteq5j

Beginner2022-11-18Added 17 answers

If n 1 and n 2 are odd then k 1 , k 2 such that n 1 = 2 k 1 + 1 and n 2 = 2 k 2 + 1
So we find:
n 1 + n 2 = ( 2 k 1 + 1 ) + ( 2 k 2 + 1 ) = 2 ( k 1 + k 2 + 1 )
which is a multiple of 2 and therefore even.
In modular arithmetic with an odd modulus all numbers are both odd and even.

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