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Cono Sur Olympiad
2021 Cono Sur Olympiad
5
5
Part of
2021 Cono Sur Olympiad
Problems
(1)
P5 Cono Sur 2021
Source: Cono Sur 2021 #5
11/30/2021
Given an integer
n
≥
3
n \geq 3
n
≥
3
, determine if there are
n
n
n
integers
b
1
,
b
2
,
…
,
b
n
b_1, b_2, \dots , b_n
b
1
,
b
2
,
…
,
b
n
, distinct two-by-two (that is,
b
i
≠
b
j
b_i \neq b_j
b
i
=
b
j
for all
i
≠
j
i \neq j
i
=
j
) and a polynomial
P
(
x
)
P(x)
P
(
x
)
with coefficients integers, such that
P
(
b
1
)
=
b
2
,
P
(
b
2
)
=
b
3
,
…
,
P
(
b
n
−
1
)
=
b
n
P(b_1) = b_2, P(b_2) = b_3, \dots , P(b_{n-1}) = b_n
P
(
b
1
)
=
b
2
,
P
(
b
2
)
=
b
3
,
…
,
P
(
b
n
−
1
)
=
b
n
and
P
(
b
n
)
=
b
1
P(b_n) = b_1
P
(
b
n
)
=
b
1
.
algebra