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PEN D Problems
6
D 6
D 6
Source:
May 25, 2007
modular arithmetic
induction
Euler
search
Congruences
Problem Statement
Show that, for any fixed integer
n
≥
1
,
\,n \geq 1,\,
n
≥
1
,
the sequence
2
,
2
2
,
2
2
2
,
2
2
2
2
,
⋯
(
m
o
d
n
)
2, \; 2^{2}, \; 2^{2^{2}}, \; 2^{2^{2^{2}}}, \cdots \pmod{n}
2
,
2
2
,
2
2
2
,
2
2
2
2
,
⋯
(
mod
n
)
is eventually constant.
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