Let-n-be-a-positive-integer-and-p-1-p-2-p-n-be-n-prime-numbers-all-larger-than-5-such-that-6-divides-p-1-2-p-2-2-p-n-2-Prove-that-6-divides-n-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 23000 by Tinkutara last updated on 24/Oct/17

Let n be a positive integer and p_1 , p_2 , ..., p_n be n prime numbers all larger than 5 such that 6 divides p_1 ^2 + p_2 ^2 + ... + p_n ^2 . Prove that 6 divides n.

$$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and}\:{p}_{\mathrm{1}} ,\:{p}_{\mathrm{2}} , \\ $$$$…,\:{p}_{{n}} \:\mathrm{be}\:{n}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{all}\:\mathrm{larger} \\ $$$$\mathrm{than}\:\mathrm{5}\:\mathrm{such}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{p}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{p}_{\mathrm{2}} ^{\mathrm{2}} \:+\:…\:+ \\ $$$${p}_{{n}} ^{\mathrm{2}} .\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{n}. \\ $$

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Let-n-be-a-positive-integer-and-p-1-p-2-p-n-be-n-prime-numbers-all-larger-than-5-such-that-6-divides-p-1-2-p-2-2-p-n-2-Prove-that-6-divides-n-

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