Determine all positive integers n for which there exists a polynomial f(x) with real coefficients, with the following properties:(1) for each integer k, the number f(k) is an integer if and only if k is not divisible by n;
(2) the degree of f is less than n.(Hungary) Géza Kós algebrapolynomialmodular arithmeticfunctionnumber theorygreatest common divisorsystem of equations