olymmath

TSTST 2017 Problem 3

  • Answer

Consider solutions to the equation x2−cx+1=f(x)g(x)x^{2}-c x+1=\frac{f(x)}{g(x)} where ff and gg are nonzero polynomials with nonnegative real coefficients. For each c>0c>0, determine the minimum possible degree of ff, or show that no such f,gf, g exist.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

n=\left\lceil\frac{\pi}{\arccos (c / 2)}\right\rceil

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

Locator tstst/2017/p3 · Tag JWZBW32ESM · Edit this page on GitHub · Keys: j next, k previous