A student is investigating the following statement about natural numbers.
“n3−nn^3 - nn3−n is a multiple of 4”
Prove, using algebra, that the statement is true for all odd numbers.
Use a counter example to show that the statement is not always true.
40 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.