An important theorem in Number Theory is Euler's Theorem,
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.
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