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Algebraic Methods

Algebraic Methods

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Question 170

A cybersecurity researcher is analyzing a specific encryption key property. They need to prove that the equation p2−4q=2p^2 - 4q = 2p2−4q=2 has no integer solutions for ppp and qqq.

The researcher starts a proof by contradiction as shown below:

"Suppose there exist integers ppp and qqq such that p2−4q=2p^2 - 4q = 2p2−4q=2. This implies that

p2=4q+2 p^2 = 4q + 2 p2=4q+2

so p2p^2p2 is even."

Complete the proof.

[5]
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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