N N\,N is an integer that is not divisible by 3. Prove that N2 N^2\,N2 is of one of the forms 9p+19p + 19p+1, 9p+49p + 49p+4 or 9p+79p + 79p+7, where p p\,p is an integer.
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.