Home Competitions AMO-Bench 2025 Problem 21
AMO-Bench 2025 Problem 21
Given that x , y , z x, y, z x , y , z { x 2 − 7 y 4 = z , 7 z 4 + ∑ k = 1 z 1 k ( 2 k − 1 ) ∑ k = 0 z − 1 1 ( k + z + 1 ) ( 2 z − k ) = ∑ i = 0 174545562 1 i ( 2 i − 1 ) ∑ i = 0 174545561 1 ( i + 174545563 ) ( 349091124 − i ) \begin{cases}
x^2 - 7y^4 = z,\\[6pt]
7z^4+ \frac{\sum_{k=1}^{z} \frac{1}{k(2k-1)}}{\sum_{k=0}^{ z-1} \frac{1}{(k+z+1)(2z-k)}}
= \frac{\sum_{i=0}^{174545562} \frac{1}{i(2i-1)}}{\sum_{i=0}^{174545561} \frac{1}{(i+174545563)(349091124-i)}}
\end{cases} ⎩ ⎨ ⎧ x 2 − 7 y 4 = z , 7 z 4 + ∑ k = 0 z − 1 ( k + z + 1 ) ( 2 z − k ) 1 ∑ k = 1 z k ( 2 k − 1 ) 1 = ∑ i = 0 174545561 ( i + 174545563 ) ( 349091124 − i ) 1 ∑ i = 0 174545562 i ( 2 i − 1 ) 1 x + y + z x+y+z x + y + z
Dataset text AMO-Bench . Open licence.
Show the answer
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 amo-bench/2025/p21 · Tag 91DW9JJCRH · Edit this page on GitHub · Keys: j next, k previous