An integer can be written in the form 3n+k3n+k3n+k, where n n\,n is an integer and k=−1k=-1k=−1, 0 or 1.
Prove, in terms of kkk, that all cube numbers are either a multiple of 9 or 1 more or one less than a multiple of 9.
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.