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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2021 China Second Round A1
2
2
Part of
2021 China Second Round A1
Problems
(1)
A nice number theory problem.
Source: 2021 China Second Round Olympiad(A1) P2
10/7/2021
Find a necessary and sufficient condition of
a
,
b
,
n
∈
N
∗
a,b,n\in\mathbb{N^*}
a
,
b
,
n
∈
N
∗
such that for
S
=
{
a
+
b
t
∣
t
=
0
,
1
,
2
,
⋯
,
n
−
1
}
S=\{a+bt\mid t=0,1,2,\cdots,n-1\}
S
=
{
a
+
b
t
∣
t
=
0
,
1
,
2
,
⋯
,
n
−
1
}
, there exists a one-to-one mapping
f
:
S
→
S
f: S\to S
f
:
S
→
S
such that for all
x
∈
S
x\in S
x
∈
S
,
gcd
(
x
,
f
(
x
)
)
=
1
\gcd(x,f(x))=1
g
cd
(
x
,
f
(
x
))
=
1
.
number theory
function