Fermat's little theorem

Proof

If \(a\) is an integer, \(p\) is a prime number, and \(a\) is not divisible by \(p,\) then \(a^{p - 1} \equiv 1 \pmod{p}\)
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If \(a\) is an integer, \(p\) is a prime number, and \(a\) is not divisible by \(p,\) then \(a^p \equiv a \pmod{p}\)

Using the theorem

Find the remainder: \(2^{50} \div 17\)
\(4\)
Find the remainder: \(4^{532} \div 11\)
\(5\)
Find the remainder: \(7^{2001} \div 5\)
Find the remainder: \(5^{3571} \div 11\)
Find the remainder: \(4^{100{,}000} \div 19\)