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Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2019 Korea National Olympiad
7
7
Part of
2019 Korea National Olympiad
Problems
(1)
Existance of such m
Source: Korea National Olympiad 2019 P7
11/16/2019
For prime
p
≡
1
(
m
o
d
7
)
p\equiv 1\pmod{7}
p
≡
1
(
mod
7
)
, prove that there exists some positive integer
m
m
m
such that
m
3
+
m
2
−
2
m
−
1
m^3+m^2-2m-1
m
3
+
m
2
−
2
m
−
1
is a multiple of
p
p
p
.
number theory