| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a straightforward proof by induction for divisibility. The base case is trivial (n=1 gives 1000+169=1169=167×7), and the inductive step requires standard algebraic manipulation to factor out 7. While it's a Further Maths topic, divisibility proofs by induction are among the most routine applications of the technique, requiring no novel insight beyond the standard template. |
| Spec | 4.01a Mathematical induction: construct proofs |
4 Prove by mathematical induction that, for all positive integers $n , 10 ^ { 3 n } + 13 ^ { n + 1 }$ is divisible by 7 .
\hfill \mbox{\textit{CAIE FP1 2006 Q4 [5]}}