Sum of consecutive integers

Number Theory Level 3

The sum of $n$ consecutive integers is a multiple of $n$ .

For what positive integers $n$ is this statement true?

n

is any positive integers

n

is multiple of 3 only

n

is even only

n

is odd only

1 solution

John Lesteя Tan
Aug 14, 2015

since the formula of the sum of integers from 1 to n is [n(n+1)]/2 , then if n is odd, it will NEVER cancel to the denominator 2
which if n is even, it will surely cancel the denominator 2

But $n+1$ will be cancelled out .

Sai Ram - 5 years, 9 months ago