Jacob believes that for all positive integers n3+3n+4n^3 + 3n + 4n3+3n+4 is a multiple of 4.
Which value of n n\,n shown below is a counter example to Jacob’s belief?
n=5n=6n=7n=8 n = 5 \quad n = 6 \quad n = 7 \quad n = 8 n=5n=6n=7n=8n=5n=5n=5
n=6n=6n=6
n=7n=7n=7
n=8n=8n=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.