MathDB
Problems
Contests
International Contests
Balkan MO Shortlist
2013 Balkan MO Shortlist
A3
A3
Part of
2013 Balkan MO Shortlist
Problems
(1)
(x^2-8x+25)(x^2-16x+100)...(x^2-8nx+25n^2)-1 not product of 2 integer polyn.
Source: Balkan MO Shortlist 2013 A3 BMO
3/9/2020
Prove that the polynomial
P
(
x
)
=
(
x
2
−
8
x
+
25
)
(
x
2
−
16
x
+
100
)
.
.
.
(
x
2
−
8
n
x
+
25
n
2
)
−
1
P (x) = (x^2- 8x + 25) (x^2 - 16x + 100) ... (x^2 - 8nx + 25n^2)- 1
P
(
x
)
=
(
x
2
−
8
x
+
25
)
(
x
2
−
16
x
+
100
)
...
(
x
2
−
8
n
x
+
25
n
2
)
−
1
,
n
∈
N
∗
n \in N^*
n
∈
N
∗
, cannot be written as the product of two polynomials with integer coefficients of degree greater or equal to
1
1
1
.
algebra
polynomial
factoring polynomials
Integer Polynomial