Home Competitions OFM 2023 S1
Let P ( X ) = a n X n + a n − 1 X n − 1 + ⋯ + a 1 X + a 0 P(X) = a_n X^n + a_{n-1} X^{n-1} + \cdots + a_1 X + a_0 P ( X ) = a n X n + a n − 1 X n − 1 + ⋯ + a 1 X + a 0 0 ⩽ a i ⩽ a 0 0 \leqslant a_i \leqslant a_0 0 ⩽ a i ⩽ a 0 i = 1 , 2 , … , n i = 1, 2, \ldots, n i = 1 , 2 , … , n P ( X ) 2 = b 2 n X 2 n + b 2 n − 1 X 2 n − 1 + ⋯ + b n + 1 X n + 1 + ⋯ + b 1 X + b 0 P(X)^2 = b_{2n} X^{2n} + b_{2n-1} X^{2n-1} + \cdots + b_{n+1} X^{n+1} + \cdots + b_1 X + b_0 P ( X ) 2 = b 2 n X 2 n + b 2 n − 1 X 2 n − 1 + ⋯ + b n + 1 X n + 1 + ⋯ + b 1 X + b 0 4 b n + 1 ⩽ P ( 1 ) 2 4 b_{n+1} \leqslant P(1)^2 4 b n + 1 ⩽ P ( 1 ) 2
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 francophone/2023/s1 · Tag M7B7968HKK · Edit this page on GitHub · Keys: j next, k previous