One of the question at HW in Number Theory was calculating $$147^{147}\mod 13$$ We didn't see much about the modular properties yet, so I am kind of stuck. Could someone give a hint or a direction how to approach it?
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I'm guessing you want to ask about $147^{147}\bmod{13}$? – hardmath Mar 21 '18 at 20:13
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Also this duplicate might be helpful. – Dietrich Burde Mar 21 '18 at 20:14
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First step: since $147\equiv 4 \bmod 13$, $147^{147}\equiv 4^{147} \bmod 13$. Then $4=2^2$ might be useful. Also look at Fermat's little theorem. – Joffan Mar 21 '18 at 23:28