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?


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

$g i v e n t h e q u a d r a t i c f u n c t i o n$ $f (x) = x + 2 + p x + q w h e r e p a n d q a r e ? i n t e g e r . s$ $l e t a, b, a n d c d i s t i n c i n t e g e r s s u c h t h a t$ $2^{2020} e v e n l y d i v i d e s f (a), f (b), a n d f (c), b u t$ $2^{1000} d o e s n o t d i v i d e b - a a n d a l s o d o e s n o t$ $d i v i d e c - a . s h o w t h a t 2^{1021} j u s t d i v i d e b - c ?$
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