Pure Mathematics A Level Maths Worksheets, Questions and Revision

Prove that the sum of any two even integers is always even.

1. Let the two even integers be 2m and 2n, where m and n are integers.
2. Form the sum: 2m + 2n.
3. Factorise: 2m + 2n = 2(m + n).
4. Since m + n is an integer, 2(m + n) is a multiple of 2, so it is even.
5. Final answer: the sum of any two even integers is always even (proved).