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2024 District Olympiad
P1
Trivial NT with a ring
Trivial NT with a ring
Source: Romanian District Olympiad 2024 12.1
March 10, 2024
Ring Theory
number theory
Problem Statement
Determine the integers
n
⩾
2
n\geqslant 2
n
⩾
2
for which the equation
x
2
−
3
^
⋅
x
+
5
^
=
0
^
x^2-\hat{3}\cdot x+\hat{5}=\hat{0}
x
2
−
3
^
⋅
x
+
5
^
=
0
^
has a unique solution in
(
Z
n
,
+
,
⋅
)
.
(\mathbb{Z}_n,+,\cdot).
(
Z
n
,
+
,
⋅
)
.
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