MathDB

Day 2

Part of 1995 Korea National Olympiad

Problems(1)

x^{n+2}+ax^{n+1}+bx^{n}+a+b cannot be decomposed

Source: Korean Mathematical Olympiad 1995, Final Round P5 FKMO

7/21/2018
Let a,ba,b be integers and pp be a prime number such that: (i) pp is the greatest common divisor of aa and bb; (ii) p2p^2 divides aa. Prove that the polynomial xn+2+axn+1+bxn+a+bx^{n+2}+ax^{n+1}+bx^{n}+a+b cannot be decomposed into the product of two polynomials with integer coefficients and degree greater than 11.
polynomialInteger Polynomialgreatest common divisorprimefactorizationalgebra