Prove that if n2 n^2\,n2 is divisible by 3, then n n\,n is divisible by 3.
Hence prove by contradiction that 3 \sqrt{3}\,3 is irrational
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.