TMUA 2017 Paper 2 Q5 — Worked Solution

P2·Number Theory & Divisibility, Logic & Quantifiers·6.0Official · 2017 · Q5

primescounterexamplemulti-statement

Consider the following three statements:

10 p^{2} + 1

and

10 p^{2} - 1

are both prime when

p

is an odd prime.

Every prime greater than

5

is of the form

6 n + 1

for some integer

n

No multiple of

7

greater than

7

is prime.

The result

91 = 7 \times 13

can be used to provide a counterexample to which of the above statements?

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