| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Proof |
| Type | Proof involving squares and modular forms |
| Difficulty | Standard +0.8 This is a proof question requiring modular arithmetic reasoning. Students must recognize that N can be written as 3k+1 or 3k+2, then expand N² for each case to show both yield the form 3p+1. While the technique is standard for A-level proof questions, it requires systematic case analysis and algebraic manipulation beyond routine exercises. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
$N$ is an integer that is not divisible by 3. Prove that $N^2$ is of the form $3p + 1$, where $p$ is an integer. [5]
\hfill \mbox{\textit{OCR PURE Q5 [5]}}