TMUA 2021 Paper 2 Q10 — Worked Solution

P2·Number Theory & Divisibility, Logic & Quantifiers·5.5Official · 2021 · Q10

counterexampleimplicationprimes

The first seven terms of a sequence of positive integers are:

u_{1} = 15, u_{2} = 21, u_{3} = 30, u_{4} = 37, u_{5} = 44, u_{6} = 51, u_{7} = 59.

Consider the following statement about this sequence:

(*)

n

is a prime number, then

u_{n}

is a multiple of

3

u_{n}

is a multiple of

5

.What is the smallest value of

n

that provides a counterexample to

(*)

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