2014/014) Demonstrate that only prime numbers (except for the "2"), can be expressed as the sum of two consecutive natural numbers.

As prime numbers > 2 are odd so it is sum of 2 consecutive numbers

Let the number of numbers be n and 1st number a+1

then sum of numbers= an + n(n+1)/2

it is integer
if n is odd (n+1)/2 is integer so it is divsible by n

if n is even an and n(n+1)/2 is divisible by n/2

so if n > 2 and odd it is not prime as divsible by n

if n > 2 and even it is divisible by n/2(which is >= 2) so not prime