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Hello, yellow4321!
Here's a rather primitive method . . .
Calculate: .$\displaystyle 5^{72} \pmod{73}$
We have: .$\displaystyle 5^9 \;=\;1,953,125 \;\equiv\;10\pmod{73}$
Then: .$\displaystyle (5^9)^8 \;\equiv\;10^8 \pmod{73} $
. . and we find that: .$\displaystyle 10^8 \;\equiv\;1\pmod{73}$
Therefore: .$\displaystyle 5^{72} \;\equiv\;1\pmod{73}$