Moderate -0.8 This question requires finding a single counterexample to disprove a statement about prime numbers. While students need to recognize that n=9 gives 2^9-1=511=7×73 (or similar), this is a straightforward disproof-by-counterexample task with minimal calculation, requiring only basic knowledge of what constitutes a valid counterexample rather than extended reasoning or proof construction.
2 Angela makes the following claim.
\begin{displayquote}
" \(n\) is an odd positive integer greater than \(1 \Rightarrow 2 ^ { n } - 1\) is prime"
\end{displayquote}
Prove that Angela's claim is false.
as \(511\) is divisible by \(7\), hence claim false
M1, A1, M1, E1
Any \(2^{\text{odd}} - 1\) that is non-prime
Counter example can be mentioned at the start
Answer
Marks
[3]
Attempt $2^n - 1$ for any odd integer $n$
eg $2^9 - 1 = 511$
This is a counter example
as $511$ is divisible by $7$, hence claim false | M1, A1, M1, E1 | Any $2^{\text{odd}} - 1$ that is non-prime
Counter example can be mentioned at the start
| [3]
---
2 Angela makes the following claim.
\begin{displayquote}
" $n$ is an odd positive integer greater than $1 \Rightarrow 2 ^ { n } - 1$ is prime"
\end{displayquote}
Prove that Angela's claim is false.
\hfill \mbox{\textit{OCR H240/02 2018 Q2 [4]}}