I've been brushing up my all-round skills since we broke up, and I'm come across a question I just cannot do; namely to prove (using induction) that 7^n - 4^n - 3^n is divisible by 12 It starts off easily enough: 7^k - 4^k - 3^k = 12A Then considering: 7^k+1 - 4^k+1 - 3^k+1, which of course is: 7(7^k) - 4(4^k) - 3(3^k) If you substitute for 7^k, you end up with: 84A + 3(4^k) + 4(3^k) which is where I'm stuck. Ahhh...... The process of typing my thoughts has helped me to spot something I haven't spotted the last half an hour. Can you start converting the 3(4^k) into a 12(4^k-1)? Is that allowed?