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International Zhautykov Olympiad
2022 International Zhautykov Olympiad
5
5
Part of
2022 International Zhautykov Olympiad
Problems
(1)
Sums Of Polynomials
Source: IZhO 2022 Day 2 Problem 5
2/18/2022
A polynomial
f
(
x
)
f(x)
f
(
x
)
with real coefficients of degree greater than
1
1
1
is given. Prove that there are infinitely many positive integers which cannot be represented in the form
f
(
n
+
1
)
+
f
(
n
+
2
)
+
⋯
+
f
(
n
+
k
)
f(n+1)+f(n+2)+\cdots+f(n+k)
f
(
n
+
1
)
+
f
(
n
+
2
)
+
⋯
+
f
(
n
+
k
)
where
n
n
n
and
k
k
k
are positive integers.
algebra
polynomial