the units digit of (43)hole power17
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clearly the unit digit must be a multiple of 3
let us find a sequence of this that is
3^1 = 3, 3^2=9, 3^3=27, 3^4=81
so we can write this unit digits as 3^4n =3,
3^4n+1 =9, 3^4n+2=7, 3^4n+3=1
were n is a multiple of 4
so now 3^17 = 3^4(4)+1 which is in the form of
3^4n+1 for which the unit digit is 9
hence 9 is the unit digit
let us find a sequence of this that is
3^1 = 3, 3^2=9, 3^3=27, 3^4=81
so we can write this unit digits as 3^4n =3,
3^4n+1 =9, 3^4n+2=7, 3^4n+3=1
were n is a multiple of 4
so now 3^17 = 3^4(4)+1 which is in the form of
3^4n+1 for which the unit digit is 9
hence 9 is the unit digit
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