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6
SMT 2023 Discrete #6
SMT 2023 Discrete #6
Source:
May 3, 2023
Problem Statement
We say that an integer
x
∈
{
1
,
…
,
102
}
x\in\{1,\dots,102\}
x
∈
{
1
,
…
,
102
}
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
i
t
a
l
i
c
′
>
s
q
u
a
r
e
−
i
s
h
<
/
s
p
a
n
>
<span class='latex-italic'>square-ish</span>
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
i
t
a
l
i
c
′
>
s
q
u
a
re
−
i
s
h
<
/
s
p
an
>
if there exists some integer
n
n
n
such that
x
≡
n
2
+
n
(
m
o
d
103
)
x\equiv n^2+n\pmod{103}
x
≡
n
2
+
n
(
mod
103
)
. Compute the product of all
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
i
t
a
l
i
c
′
>
s
q
u
a
r
e
−
i
s
h
<
/
s
p
a
n
>
<span class='latex-italic'>square-ish</span>
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
i
t
a
l
i
c
′
>
s
q
u
a
re
−
i
s
h
<
/
s
p
an
>
integers modulo
103
103
103
.
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