MathDB

1

Part of 2021 Final Mathematical Cup

Problems(2)

diophantine 2x^2 + 5xy + 2y^2 = n

Source: 2021 3nd Final Mathematical Cup Junior Division P1 FMC

10/13/2021
Find all integer nn such that the equation 2x2+5xy+2y2=n2x^2 + 5xy + 2y^2 = n has integer solution for xx and yy.
number theoryDiophantine equationdiophantine
f(n)f(m)=f ((nm)^{2021})

Source: 2021 3nd Final Mathematical Cup Senior Division P1 FMC

10/30/2022
Let NN is the set of all positive integers. Determine all mappings f:N−{1}→Nf: N-\{1\} \to N such that for every n≠mn \ne m the following equation is true f(n)f(m)=f((nm)2021)f(n)f(m)=f\left((nm)^{2021}\right)
functionalfunctional equationalgebra