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\( 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\( 13^4 = (169)^2 \equiv (16)^2 = 256 \equiv 256 - 15\cdot17 = 256 - 255 = 1 \) → yes\( 14^4 = (-3)^4 = 81 \equiv 13\( 15^4 = (-2)^4 = 16\( 16^4 = (-1)^4 = 1 \), but \( 16 \equiv -1 \), excluded