which is valid for relatively prime a and n. The Euler Function,
(n), is defined to be
where
p1,
p2, ... are the prime
factors of n.Solution
An important theorem in Number Theory is Euler's Theorem,
namely,
which is valid for relatively prime a and n. The
Euler Function, (n), is defined to be
where
p1,
p2, ... are the prime
factors of n.
Notice that (100) = 40. Then,
by Euler's Theorem,
340 leaves a remainder
of 1 when divided by 100. Therefore,
340 ends in 01.
340 is 12,157,665,459,056,928,801, which does indeed end in 01.