Proof by deduction and exhaustionAQA A-Level Maths: Mind map

Exam questions on Proof by deduction and exhaustion

1. Let $n$ be a positive integer.
   Show that the sum of the three consecutive integers $n$, $n+1$ and $n+2$ is a multiple of 3.2 marks
2. Every integer has the form $3k$, $3k+1$ or $3k+2$, where $k$ is an integer.
   Hence prove that the square of any integer is either a multiple of 3 or one more than a multiple of 3.2 marks
3. A student wants to prove that $n^3-n$ is divisible by 6 for every positive integer $n$.
   Factorise $n^3-n$ fully and use your factorisation to explain why it is always even.3 marks