Prove that the following statement is not true.
m m\,m is an odd number greater than 1 ⇒m2+4\Rightarrow m^2 + 4⇒m2+4 is prime.
By considering separately the case when n n\,n is odd and the case when n n\,n is even, prove that the following statement is true.
n n\,n is a positive integer ⇒n2+1\Rightarrow n^2 + 1⇒n2+1 is not a multiple of 4.
39 exam-style questions on Edexcel AS 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.