Given that n n\,n is an integer and an odd integer is 2n+12n+12n+1, write down an expression for the next odd integer.
Hence prove that the sum of the squares of two consecutive odd integers is always 2 more than a multiple of 8.
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.