Home Competitions NO-ABEL 2018 Problem 4
Find all polynomials P P P P ( x ) + ( 2018 2 ) P ( x + 2 ) + . . . + ( 2018 2106 ) P ( x + 2016 ) + P ( x + 2018 ) = P(x) + \binom{2018}{2}P(x+2)+...+\binom{2018}{2106}P(x+2016)+P(x+2018)= P ( x ) + ( 2 2018 ) P ( x + 2 ) + ... + ( 2106 2018 ) P ( x + 2016 ) + P ( x + 2018 ) = = ( 2018 1 ) P ( x + 1 ) + ( 2018 3 ) P ( x + 3 ) + . . . + ( 2018 2105 ) P ( x + 2015 ) + ( 2018 2107 ) P ( x + 2017 ) =\binom{2018}{1}P(x+1)+\binom{2018}{3}P(x+3)+...+\binom{2018}{2105}P(x+2015)+\binom{2018}{2107}P(x+2017) = ( 1 2018 ) P ( x + 1 ) + ( 3 2018 ) P ( x + 3 ) + ... + ( 2105 2018 ) P ( x + 2015 ) + ( 2107 2018 ) P ( x + 2017 ) x x x
Dataset text AI-MO AoPS . Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Add a solution
Similar problems
These problems have the most words in common with this statement.
Locator no-abel/2018/p4 · Tag CFVZ5XDHAX · Edit this page on GitHub · Keys: j next, k previous