Prove by contradiction that there are infinitely many prime numbers, using
N=(p1×p2×p3×⋯×pn)+k, N=(p_1\times p_2\times p_3\times\dots\times p_n)+k, N=(p1×p2×p3×⋯×pn)+k,where k k\,k is a positive integer such that gcd(k,pi)=1\gcd(k,p_i)=1gcd(k,pi)=1 for i=1,2,…,ni=1,2,\dots,ni=1,2,…,n.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.