| Exam Board | SPS |
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| Module | SPS SM Pure (SPS SM Pure) |
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| Year | 2025 |
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| Session | February |
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| Topic | Proof |
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7. (i) Prove by counter example that the statement
"If \(n\) is a prime number then \(3 ^ { n } + 2\) is also a prime number."
is false.
(ii) Use proof by exhaustion to prove that if \(m\) is an integer that is not divisible by 3 , then
$$m ^ { 2 } - 1$$
is divisible by 3
(3)
(Total for Question 7 is 5 marks)