Answer to Question #349806 in Discrete Mathematics for janine

Question #349806

Use a direct proof to show that the sum of two odd integers(k and l) is even.


1
Expert's answer
2022-06-13T12:03:23-0400

Proof.

Let kk and ll be the odd integers. Then there exist some integers k0k_0 and l0l_0 such that

k=2k0+1,k=2k_0+1,

l=2l0+1.l=2l_0+1.

We can find the sum:

k+l=(2k0+1)+(2l0+1)=2k0+2l0+2=2(k0+l0+1),k+l=(2k_0+1)+(2l_0+1)=2k_0+2l_0+2=2(k_0+l_0+1),

where k0+l0+1k_0+l_0+1 is an integer as a sum of integers.

So k+lk+l is divisible by 2 and is even.

The proof is finished.


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