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Two Irrational Numbers from the Last Nonzero Digits of \(n!\) and \(n^n\)

by Gregory Dresden

This article originally appeared in:
Mathematics Magazine
October, 2001

Subject classification(s): Algebra and Number Theory | Number Theory | Irrational Numbers
Applicable Course(s): 4.3 Number Theory

The author considers two infinite decimals, where the \(n\)th digit is the last non-zero digit of \(n!\), creating the number \(F\), and using \(n^n\), creating the number \(P\). The author shows that both \(F\) and \(P\) are irrational.

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Capsule Course Topic(s):
Number Theory | Irrationality
Number Theory | Numbers With Special Forms or Properties, Base Representation and Decimal Expansion
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