Let-p-q-be-prime-numbers-such-that-n-3pq-n-is-a-multiple-of-3pq-for-all-positive-integers-n-Find-the-least-possible-value-of-p-q-

Tinku Tara June 4, 2023 Number Theory 0 Comments

Question Number 21229 by Tinkutara last updated on 16/Sep/17

Let p, q be prime numbers such that n^(3pq) − n is a multiple of 3pq for all positive integers n. Find the least possible value of p + q.

$$\mathrm{Let}\:{p},\:{q}\:\mathrm{be}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${n}^{\mathrm{3}{pq}} \:−\:{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}{pq}\:\mathrm{for}\:\boldsymbol{\mathrm{all}} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:{n}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{p}\:+\:{q}. \\ $$

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Let-p-q-be-prime-numbers-such-that-n-3pq-n-is-a-multiple-of-3pq-for-all-positive-integers-n-Find-the-least-possible-value-of-p-q-

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