Assume there is a finite number of prime numbers: p1,p2,p3,…,pnp_1, p_2, p_3, \dots, p_np1,p2,p3,…,pn. Construct the number N=(p1×p2×p3×⋯×pn)+1N = (p_1 \times p_2 \times p_3 \times \dots \times p_n) + 1N=(p1×p2×p3×⋯×pn)+1 and explain why dividing N N\,N by any of the primes p1,…,pn p_1, \dots, p_n\,p1,…,pn leaves a remainder of 1.
Prove by contradiction that there are infinitely many prime numbers
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.