give answer of question number 169 with explanation
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7^1=7,
the units digit is 7
7^2 = 49, the units digit is 9.
And without evaluating
the powers, one can see that the unit digit of 7^3 is 3,
and that of 7^4 is 1.
Now if you continue, you will end up with the same values in the same order, 7, 9,3, 1.
In fact, 7^n = 7 iff n = 4k+1.
Similarly, it equals 9
iff n = 4k+2, 3 iff n = 4k+3, and1 iff n = 4k.25 being congruent to 1 mod 4,
7^25 has unit digit equal to 7.
the units digit is 7
7^2 = 49, the units digit is 9.
And without evaluating
the powers, one can see that the unit digit of 7^3 is 3,
and that of 7^4 is 1.
Now if you continue, you will end up with the same values in the same order, 7, 9,3, 1.
In fact, 7^n = 7 iff n = 4k+1.
Similarly, it equals 9
iff n = 4k+2, 3 iff n = 4k+3, and1 iff n = 4k.25 being congruent to 1 mod 4,
7^25 has unit digit equal to 7.
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