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Japan MO Finals
1999 Japan MO Finals
4
4
Part of
1999 Japan MO Finals
Problems
(1)
Function
Source: Japan 99
2/5/2004
Prove that the polynomial
f
(
x
)
=
(
x
2
+
1
)
(
x
2
+
2
2
)
⋯
(
x
2
+
n
2
)
+
1
f(x)=(x^2+1)(x^2+2^2)\cdots (x^2+n^2)+1
f
(
x
)
=
(
x
2
+
1
)
(
x
2
+
2
2
)
⋯
(
x
2
+
n
2
)
+
1
cannot be expressed as a product of two polynomials with integer coefficients with degree greater than
1
1
1
.
function
algebra
polynomial
algebra unsolved