Question

N is a positive integer. Explain why n(n-1) must be an even number.

Answer 1

Let me assign n a number: 3 an easy value we can work with. If we substitute it into the equation we get:

3 * (3-1). According to BIDMAS/BODMAS, we must first work out the brackets and then multiple it by the 3.

Do 3-1 = 2, 2*3 = 6 which is an even number. If we try with an even number we also get an even number:

4-1 = 3, 3*4 = 12. Even if we try this with a number like 7, 9 or 10 - we will always get an even integer, this is because, whenever we multiple an even number with an even or odd number - we always get an even number. So when we take away 1 by an even number, and multiple it with an odd number, we get even. Same applies to when we take away an odd number by 1 to get an even number and then times it by an odd number - we always get even.