| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 4 |
| Topic | Proof |
| Type | Prime number conjectures |
| Difficulty | Challenging +1.2 This requires recognizing that 2^n - 1 factors as (2^(n/2) - 1)(2^(n/2) + 1) when n is even, then showing both factors exceed 1. It's a straightforward proof by factorization using difference of squares, more demanding than routine algebra but less challenging than multi-step problem-solving or complex geometric proofs. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01d Proof by contradiction |
Shona makes the following claim.
"$n$ is an even positive integer greater than $2 \Rightarrow 2^n - 1$ is not prime"
Prove that Shona's claim is true. [4]
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q6 [4]}}