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.
Practise Edexcel AS Level Maths Algebraic Methods with exam-style questions for AS Level Maths. 35 questions covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.