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Periodicity of Euler Numbers in Modular Arithmetic

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m
41
The Euler numbers
E
n
are integers that arise in the series expansion of the hyperbolic secant function
sech
around the origin:
sech(x)
∞
∑
n=0
n
x
E
n
/n!
. The plot above indicates that the sequence
c
n
E
2n
(modm)
is periodic in
n
for any integer
m>1
. Incidentally, the sequence
n
(-1)
E
2n
(modm)
is periodic with respect to
n
.
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