Jacob believes that for all positive integers n3+n+2n^3 + n + 2n3+n+2 is a multiple of 4.
k k\,k is a positive integer and a multiple of 4.
Which value of n n\,n shown below is a counter example to Jacob’s belief?
n=2n=2n=2
n=3n=3n=3
n=kn=kn=k
n=5n=5n=5
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.