if a and b are odd then a + b is even

if a and b are odd then a + b is even

Let a and b be positive odd integers of the form:

• a = 2n + 1
• b = 2m + 1

a + b = 2n + 1 + 2m + 1
a + b = 2n + 2m + 1 + 1

Combing like terms, we get:
a + b = 2n + 2m + 2
a + b = 2(n + m) + 2

Let k = n + m
a + b = 2k + 2

Therefore a + b is even