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Algebraic Methods

Algebraic Methods

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Question 32
a.

Assume there are a finite number of prime numbers. Let x x\,x be the product of all prime numbers:

x=p1×p2×p3×⋯×pn x = p_1 \times p_2 \times p_3 \times \dots \times p_n x=p1​×p2​×p3​×⋯×pn​

Consider y=x+1y = x + 1y=x+1. Explain why y y\,y has no prime factors from p1 p_1\,p1​ to pnp_npn​.

[4]
b.

Hence prove by contradiction that there are infinitely many prime numbers

[2]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

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.

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