| Exam Board | SPS |
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| Module | SPS SM Pure (SPS SM Pure) |
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| Year | 2022 |
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| Session | June |
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| Topic | Proof |
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15. a)
Prove that
$$n - 1 \text { is divisible by } 3 \Rightarrow n ^ { 3 } - 1 \text { is divisible by } 9$$
b)
Show that if \(\log _ { 2 } 3 = \frac { p } { q }\), then
$$2 ^ { p } = 3 ^ { q }$$
Use proof by contradiction to prove that \(\log _ { 2 } 3\) is irrational.
[0pt]
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