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2
SMT 2022 Discrete Tiebreaker #2
SMT 2022 Discrete Tiebreaker #2
Source:
April 1, 2023
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be the solutions to
x
3
+
3
x
2
−
1
=
0
x^3+3x^2-1=0
x
3
+
3
x
2
−
1
=
0
. Define
S
n
=
a
n
+
b
n
+
c
n
S_n=a^n+b^n+c^n
S
n
=
a
n
+
b
n
+
c
n
. Given that there are integers
0
≤
i
,
j
,
k
≤
36
0\le i,j,k\le36
0
≤
i
,
j
,
k
≤
36
such that
S
n
≡
i
n
+
j
n
+
k
n
(
m
o
d
37
)
S_n\equiv i^n+j^n+k^n\pmod{37}
S
n
≡
i
n
+
j
n
+
k
n
(
mod
37
)
for all positive integer
n
n
n
, determine the product
i
j
k
ijk
ijk
.
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