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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
10.5
x^{1999}+x^{1998}+...+x^3+x^2+ax+b (VI Soros Olympiad 1990-00 R1 10.5)
x^{1999}+x^{1998}+...+x^3+x^2+ax+b (VI Soros Olympiad 1990-00 R1 10.5)
Source:
May 28, 2024
algebra
polynomial
Problem Statement
Prove that the polynomial
x
1999
+
x
1998
+
.
.
.
+
x
3
+
x
2
+
a
x
+
b
x^{1999}+x^{1998}+...+x^3+x^2+ax+b
x
1999
+
x
1998
+
...
+
x
3
+
x
2
+
a
x
+
b
for any real values of the coefficients
a
>
b
>
0
a>b>0
a
>
b
>
0
does not have an integer root.
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