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Question 43

In the field of cryptography, certain protocols rely on the property that specific constants are not rational. Let $S\,$ be a constant defined by the equation $S^2 - 13 = 0$ . Given that $S > 0$ , prove by contradiction that $S\,$ is an irrational number.

(You may assume that if $n^2\,$ is a multiple of 13, then $n\,$ is also a multiple of 13 for any integer $n$ .)

[6]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof

132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 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 43

(You may assume that if $n^2\,$ is a multiple of 13, then $n\,$ is also a multiple of 13 for any integer $n$ .)

[6]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof