A student is investigating the following statement about natural numbers.
“n3−nn^3 - nn3−n is a multiple of 4”
Given that the statement is true for a particular value of nnn, prove, using algebra, that n n\,n cannot be of the form 4k+24k+24k+2, where k k\,k is a non-negative integer.
Use a counter example to show that n n\,n does not have to be odd.
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.