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1.1 Proof

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Question 51

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

The researcher starts a proof by contradiction as shown below:

"Suppose there exist integers $p$ and $q$ such that $p^2 - 4q = 2$ . This implies that

p^2 = 4q + 2

so $p^2$ is even."

Complete the proof.

[5]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof

107 exam-style questions on OCR A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Logical connectives, 1.1.3 Disproof by counter example, 1.1.4 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.

1.1 Proof

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1.1 Proof

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Question 51

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

The researcher starts a proof by contradiction as shown below:

"Suppose there exist integers $p$ and $q$ such that $p^2 - 4q = 2$ . This implies that

p^2 = 4q + 2

so $p^2$ is even."

Complete the proof.

[5]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof