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China Northern MO
2022 China Northern MO
2
2
Part of
2022 China Northern MO
Problems
(1)
221|3^a -2^a, n and n+1 lie in {n\in N^*: 211|1+2^n+3^n+4^n}
Source: China Northern MO 2022 p2 CNMO
10/28/2022
(1) Find the smallest positive integer
a
a
a
such that
221
∣
3
a
−
2
a
221|3^a -2^a
221∣
3
a
−
2
a
,(2) Let
A
=
{
n
∈
N
∗
:
211
∣
1
+
2
n
+
3
n
+
4
n
}
A=\{n\in N^*: 211|1+2^n+3^n+4^n\}
A
=
{
n
∈
N
∗
:
211∣1
+
2
n
+
3
n
+
4
n
}
. Are there infinitely many numbers
n
n
n
such that both
n
n
n
and
n
+
1
n+1
n
+
1
belong to set
A
A
A
?
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