Prove n^3-n is multiple of 6 for all n
factoring gives form n(n+1)(n-1) from here it should be realised that if n is not a multiple of 3 then n-1 is or n+1 is as multiples of 3 go up in 3s. Hence one of the values either n,n-1 or n+1 must be multiple of 3.
AN
Related Maths GCSE answers
All answers ▸How do I add two fractions? (plus example)
Expand (x+2)(x-3)(x+4)^2
Nadia has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change I will buy more pencils.” How many pencils and how many rulers does she buy?
What is mathematics and why should I study it?