MathDB

1

Part of 2020 Final Mathematical Cup

Problems(2)

Divisors and Perfect Squares

Source: 2nd Final Mathematical Cup Junior Division P1 (2020)

10/1/2020
Let nn be a given positive integer. Prove that there is no positive divisor dd of 2n22n^2 such that d2n2+d3d^2n^2+d^3 is a square of an integer.
number theoryDivisorsPerfect Squares
Slightly Nested FE

Source: 2nd Final Mathematical Cup Senior Division P1 (2020)

10/1/2020
Find all such functions f:Rā†’Rf:\mathbb{R} \to \mathbb{R} that for any real x,yx,y the following equation is true. f(f(x)+y)+1=f(x2+y)+2f(x)+2yf(f(x)+y)+1=f(x^2+y)+2f(x)+2y
algebrafunctional equationFunctional EquationsFunctional equation in R