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Question 89

In a specific cryptographic protocol, a validation factor $V$ is calculated for prime numbers $p$ using the formula

V(p) = p^2 - 1

Prove that for every prime number $p$ in the range $10 < p < 20$ , the validation factor $V (p)$ is a multiple of 24.

[3]

ii.

A software engineer claims that for any non-negative integer $n$ , the processing time $T(n) = n^2 + 3n + 5$ microseconds is never a multiple of 2. Use proof by contradiction to show that this claim is correct.

[4]

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 89

In a specific cryptographic protocol, a validation factor $V$ is calculated for prime numbers $p$ using the formula

V(p) = p^2 - 1

Prove that for every prime number $p$ in the range $10 < p < 20$ , the validation factor $V (p)$ is a multiple of 24.

[3]

ii.

[4]

Markscheme

1.1 Proof Questions

A Level
Maths
1.1 Proof