Question

“The product of two consecutive positive integers is divisible by 2”. Is this statement
true or false? Give reasons.

Answer 1

@genius12

Answer 2

2 consecutive positive integers means one integer must be even and the other must be odd

all even numbers are divisible by 2

when you multiply the odd and even together, you can still divide out the 2 from the even number

Answer 3

False.

1*3 = 3 <- not even lol.

Answer 4

consecutive?

Answer 5

Ok..

Answer 6

True. There will be an even and odd, so of course their product will be divisible by 2.

Answer 7

Yes ok guys I think @goformit100 gets the idea here. we don't all need to crowd around the same question. move on to other questions.

Answer 8

Goformit, is it clear to you?

Answer 9

You can take cases here.

Case 1 : a is even.

a = 2q (using euclid's division algorithm, q is positive integer)

\(\bf{\cfrac{a(a+1)}{2} = \cfrac{2q(a+1)}{2} = q(a+1)}\) , which is a positive integer. So,

a(a+1) is divisible by 2.

Case 2 : a + 1 is even

\(\bf{\cfrac{a(a+1)}{2} = \cfrac{2q(a)}{2} = aq}\) which is also an integer

So, a(a+1) is divisible by 2.

Answer 10

Thank you Users :)

Answer 11

You are welcome :)