MathDB
Problems
Contests
National and Regional Contests
India Contests
NMTC
2017 NMTC Junior
5
5
Part of
2017 NMTC Junior
Problems
(1)
Eisenstein? And Combi
Source: NMTC 2017 Juniors P5
10/28/2017
(a) Prove that
x
4
+
3
x
3
+
6
x
2
+
9
x
+
12
x^4+3x^3+6x^2+9x+12
x
4
+
3
x
3
+
6
x
2
+
9
x
+
12
cannot be expressed as product of two polynomials of degree 2 with integers coefficients.(b)
2
n
+
1
2n+1
2
n
+
1
segments are marked on a line. Each of these segments intersects at least
n
n
n
other segments. Prove that one of these segments intersects all other segments.
polynomial
combinatorics