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?