A common technique for finding modulo \(10\) of any huge number in the form \(a^b\)?

A common technique for finding modulo \(10\) of any huge number in the form \(a^b\)?

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OK, I'm gonna change the topic to something else:\[39^{39} \equiv n\pmod{100}\]

\(n\) has to be a two-digit number.
(I actually have to find the last two digits)

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