1) if n is not a prime number, at least n can be written as n=a b where a and b ∈N, if a=b, a=√n, n divisible by √n, if a≠b,

a and b are not both >√n, find the smaller one, n is divisible by the smaller one who is smaller than √n.

2) if n= a b, where a is a prime number, and b isn't divisible by a. we can get p= a c, q= b d, where c and d are prime numbers and isn't divisible by a or d.

hence n is divisible by pq, but not by p or q

3) n³+1 = (n+1)(n²-n+1) 2 is a special case when n²-n+1=1