Question

For which k is it true that the sum of k consecutive integers is always divisible by k?

Answer 1

Explanation:

We have two consecutive even integers:

a and b.

We know that we can write a even integer as:

a = 2*n

where n is an integer.

Then the consecutive integer to a, b, will be:

b = 2*n + 2.

Then the sum of a and b is:

a + b = 2n + 2n + 2 = 4*n + 2 = 2*(2n + 1) = k.

The next two consecutive integers greater than b will be:

c = 2n + 4

d = 2n + 6

then:

c + d = (2n + 4) + (2n + 6) = 4n + 10 = k + 4.

I hope i helped:D