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\( 4^4 = (16)^2 = (-1)^2 = 1 \mod 17 \) â yes

\( 5^4 = 625 \). \( 625 \div 17 \): \( 17 \cdot 36 = 612 \), \( 625 - 612 = 13

\( 6^4 = (36)^2 \equiv (-5)^2 = 25 \equiv 8

\( 7^4 = (49)^2 \equiv (49 - 2\cdot17 = 15)^2 = 225 \equiv 225 - 13\cdot17 = 225 - 221 = 4

\( 8^4 = (64)^2 \equiv (64 - 3\cdot17 = 13)^2 = 169 \equiv 169 - 9\cdot17 = 169 - 153 = 16

\( 9^4 = (81)^2 \equiv (81 \mod 17 = 13)^2 = 169 \equiv 16

\( 10^4 = (100)^2 \equiv (100 - 5\cdot17 = 15)^2 = 225 \equiv 4

\( 11^4 = (121)^2 \equiv (121 - 7\cdot17 = 121 - 119 = 2)^2 = 4

\( 12^4 = (144)^2 \equiv (144 - 8\cdot17 = 144 - 136 = 8)^2 = 64 \equiv 13

\( 13^4 = (169)^2 \equiv (16)^2 = 256 \equiv 256 - 15\cdot17 = 256 - 255 = 1 \) â yes

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