The last four digits of 16¹⁶
On the math-fun mailing list, Dick Hess posted “a couple of curiosities”:
A speaker at G4G16 noted that \(16^{16}\) ends in \(1616\).
A friend sent me this: \(499^{499}\) ends in \(499499\).
Are there any other cases including numbers with more digits?
That does make me curious! I’ve kept that email in my inbox since March, hoping to have a go at finding more examples when I get some free time. Nobody else responded to the email, which is usually a sign that an answer is hard to find.
At first glance, it might seem really hard to even check these facts: \(16^{16}\) is a very…
The skinny
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