MathDB
Eisenstein? And Combi

Source: NMTC 2017 Juniors P5

October 28, 2017
polynomialcombinatorics

Problem Statement

(a) Prove that x4+3x3+6x2+9x+12x^4+3x^3+6x^2+9x+12 cannot be expressed as product of two polynomials of degree 2 with integers coefficients.
(b) 2n+12n+1 segments are marked on a line. Each of these segments intersects at least nn other segments. Prove that one of these segments intersects all other segments.
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