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

Tinku Tara June 4, 2023 None 0 Comments

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

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 also does not divide c−a.show that 2^(1021) just divide b−c?

$${given}\:{the}\:{quadratic}\:{function}\: \\ $$$${f}\left({x}\right)={x}+\mathrm{2}+{px}+{q}\:{where}\:{p}\:{and}\:{q}\:{are}?{integer}.{s} \\ $$$${let}\:{a},{b},\:{and}\:{c}\:{distinc}\:{integers}\:{such}\:{that} \\ $$$$\mathrm{2}^{\mathrm{2020}} \:\:{evenly}\:{divides}\:{f}\left({a}\right),{f}\left({b}\right),{and}\:{f}\left({c}\right),{but} \\ $$$$\mathrm{2}^{\mathrm{1000}} \:{does}\:{not}\:{divide}\:{b}−{a}\:{and}\:{also}\:{does}\:{not} \\ $$$${divide}\:{c}−{a}.{show}\:{that}\:\mathrm{2}^{\mathrm{1021}} \:{just}\:{divide}\:{b}−{c}? \\ $$

Facebook Tweet Pin

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

Leave a Reply Cancel reply