1.1.4 Proof by contradiction (A-level only)

A digital signal processor generates a sequence of values based on prime numbers. Prove that for all prime numbers, $p$ , such that $\le p \le 13$ ,

p^2 - 1 \text{ is a multiple of } 24

[3]

ii.

Use proof by contradiction to show that for any positive integer $n$ ,

n^2 + 2 \text{ is not a multiple of } 4

[4]

1.1.4 Proof by contradiction (A-level only) Questions

A digital signal processor generates a sequence of values based on prime numbers. Prove that for all prime numbers, $p$ , such that $\le p \le 13$ ,

p^2 - 1 \text{ is a multiple of } 24

[3]

ii.

Use proof by contradiction to show that for any positive integer $n$ ,

n^2 + 2 \text{ is not a multiple of } 4

[4]