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Serbia Team Selection Test
1980 Yugoslav Team Selection Test
Problem 2
a modular polynomial
a modular polynomial
Source: Yugoslav TST 1980 P2
May 29, 2021
number theory
algebra
polynomial
Problem Statement
Let
a
,
b
,
c
,
m
a,b,c,m
a
,
b
,
c
,
m
be integers, where
m
>
1
m>1
m
>
1
. Prove that if
a
n
+
b
n
+
c
≡
0
(
m
o
d
m
)
a^n+bn+c\equiv0\pmod m
a
n
+
bn
+
c
≡
0
(
mod
m
)
for each natural number
n
n
n
, then
b
2
≡
0
(
m
o
d
m
)
b^2\equiv0\pmod m
b
2
≡
0
(
mod
m
)
. Must
b
≡
0
(
m
o
d
m
)
b\equiv0\pmod m
b
≡
0
(
mod
m
)
also hold?
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