If n > 3 is not prime, show that we can find positive integers a, b, c, such that n = ab + bc + ca + 1.
Solution
Trivial.
If n is not prime, then we have n = AB with A, B > 1. But AB = (A - 1)(B - 1) + (B - 1)1 + 1(A - 1) + 1.
© John Scholes
jscholes@kalva.demon.co.uk
12 Dec 1998