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Great! This shows that the sum of odd numbers is always even, where is an even number.
Likewise, it is also true that the sum of odd numbers is always odd, where is an odd number.
Relevant wiki: Even and Odd Numbers
An odd number plus an odd number is always even; for example 1 + 3 = 4 . Odds leave 1 when divided by 2, so summing two of them leaves 2 (equivalent to 0) when divided by 2.
Here's a more formal way to look at things. An odd number is 1 more than a multiple of 2. So, two odd numbers look like 2 a + 1 and 2 b + 1 . Then, their sum is ( 2 a + 1 ) + ( 2 b + 1 ) = 2 a + 2 b + 2 = 2 ( a + b + 1 ) , which is a multiple of 2. In other words, their sum is even.