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National and Regional Contests
PEN Problems
PEN D Problems
5
5
Part of
PEN D Problems
Problems
(1)
D 5
Source:
5/25/2007
Prove that for
n
≥
2
n\geq 2
n
≥
2
,
2
2
⋯
2
⏟
n
terms
≡
2
2
⋯
2
⏟
n
−
1
terms
(
m
o
d
n
)
.
\underbrace{2^{2^{\cdots^{2}}}}_{n\text{ terms}}\equiv \underbrace{2^{2^{\cdots^{2}}}}_{n-1\text{ terms}}\; \pmod{n}.
n
terms
2
2
⋯
2
≡
n
−
1
terms
2
2
⋯
2
(
mod
n
)
.
modular arithmetic
Congruences