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Kvant 2020
M2592
M2592
Part of
Kvant 2020
Problems
(1)
Integers that cannot be represented in a certain manner
Source: Kvant Magazine No. 2 2020 M2592
3/10/2023
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial taking integer values at integer inputs. Are there infinitely many natural numbers that are not representable in the form
P
(
k
)
ā
2
n
P(k)-2^n
P
(
k
)
ā
2
n
where
n
n{}
n
and
k
k{}
k
are non-negative integers?Proposed by F. Petrov
number theory
polynomial
Kvant