MathDB

1

Part of 2009 Turkey Team Selection Test

Problems(2)

Turkey TST 2009 Functional Equation

Source: Turkey TST 2009, Problem 1

4/5/2009
Find all f: Q^ \plus{} \to\ Z functions that satisfy f \left(\frac {1}{x} \right) \equal{} f(x) and (x \plus{} 1)f(x \minus{} 1) \equal{} xf(x) for all rational numbers that are bigger than 1.
functionalgorithmnumber theoryEuclidean algorithmcontinued fractionalgebrafunctional equation
Turkey TST polynominal with integer coefficients

Source: Turkey TST 2009, Problem 4

4/5/2009
For which p p prime numbers, there is an integer root of the polynominal 1 \plus{} p \plus{} Q(x^1)\cdot\ Q(x^2)\ldots\ Q(x^{2p \minus{} 2}) such that Q(x) Q(x) is a polynominal with integer coefficients?
algebrapolynomialabstract algebranumber theoryprime numbersalgebra unsolved