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Baltic Way
2015 Baltic Way
16
Polynomial
Polynomial
Source: Baltic Way 2015
November 8, 2015
polynomial
algebra
number theory
Problem Statement
Denote by
P
(
n
)
P(n)
P
(
n
)
the greatest prime divisor of
n
n
n
. Find all integers
n
≥
2
n\geq 2
n
≥
2
for which
P
(
n
)
+
⌊
n
⌋
=
P
(
n
+
1
)
+
⌊
n
+
1
⌋
P(n)+\lfloor\sqrt{n}\rfloor=P(n+1)+\lfloor\sqrt{n+1}\rfloor
P
(
n
)
+
⌊
n
⌋
=
P
(
n
+
1
)
+
⌊
n
+
1
⌋
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