N N\,N is an integer and N2 N^2\,N2 is of the form 3p+13p + 13p+1, where p p\,p is an integer. Prove that N N\,N is not divisible by 3.
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.