given-the-quadratic-function-f-x-x-2-px-q-where-p-and-q-are-integer-s-let-a-b-and-c-distinc-integers-such-that-2-2020-evenly-divides-f-a-f-b-and-f-c-but-2-1000-does-not-divide-b-a-and-als

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Question Number 115011 by joki last updated on 23/Sep/20

$$giventhequadraticfunction$$$$f\left(x\right)=x+2+px+qwherepandqare?integer.s$$$$leta,b,andcdistincintegerssuchthat$$$$2^{2020}evenlydividesf\left(a\right),f\left(b\right),andf\left(c\right),but$$$$2^{1000}doesnotdivideb-aandalsodoesnot$$$$dividec-a.showthat{2}^{1021}justdivideb-c?$$

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