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+2so p2p^2p2 is even."
Complete the proof.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
