<s>[INST] Simplest method to find $5^{20}$ modulo $61$ What is the simplest method to go about finding the remainder of $5^{20}$ divided by $61$?
 [/INST] $5^3 = 125 \equiv 3 \mod 61$, so $5^5 \equiv 25 \times 3 = 75 \equiv 14 \mod 61$,
$5^{10} \equiv 14^2 = 196 \equiv 13 \mod 61$, $5^{20} \equiv 13^2 = 169 \equiv 47 \mod 61$.
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