MathDB

Prove there exist two relatively prime polynomials

P(x),Q(x)

having integer coefficients and a real number

u>0

such that if for positive integers

a,b,c,d

we have:

|\frac{a}{c}-1|^{2021} \le \frac{u}{|d||c|^{1010}}

| (\frac{a}{c})^{2020}-\frac{b}{d}| \le \frac{u}{|d||c|^{1010}}

Then we have :

bP(\frac{a}{c})=dQ(\frac{a}{c})

(Two polynomials are relatively prime if they don't have a common root)
Proposed by Navid Safaii and Alireza Haghi

Problem Statement