We know that the cyclicity power (a^n) of 17 is 4.
[tex]\sf \longmapsto\bigg( \dfrac{17}{4}\bigg) = 1[/tex]
[tex]\sf \longmapsto17^{(17/4)}[/tex]
[tex]\sf \longmapsto17 {}^{} [/tex]
[tex]\sf \longmapsto7(last \: digit )[/tex]