Determine-whether-there-exists-2016-distinct-prime-numbers-p-1-p-2-p-2016-and-positive-integer-n-such-that-i-1-2016-1-p-i-2-1-1-n-2-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 153899 by mathdanisur last updated on 11/Sep/21

Determine whether there exists 2016 distinct prime numbers p_1 ,p_2 ,...,p_(2016) and positive integer n such that: Σ_(i=1) ^(2016) (1/(p_i ^2 + 1)) = (1/n^2 )

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{there}\:\mathrm{exists}\:\:\mathrm{2016} \\ $$$$\mathrm{distinct}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}_{\mathrm{1}} ,\mathrm{p}_{\mathrm{2}} ,…,\mathrm{p}_{\mathrm{2016}} \\ $$$$\mathrm{and}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\mathrm{2016}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{p}_{\boldsymbol{\mathrm{i}}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} } \\ $$

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Determine-whether-there-exists-2016-distinct-prime-numbers-p-1-p-2-p-2016-and-positive-integer-n-such-that-i-1-2016-1-p-i-2-1-1-n-2-

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