Remainder (1)

Algebra Level 2

If $\large x$ is a positive integer, which of the following could be the remainder when $\large 2017^x$ divided by $\large 10$ ? Add all possible remainders.

$A. 0$ .

$B. 1$ .

$C. 2$ .

$D. 3$ .

$E. 4$ .

$F. 5$ .

$G. 6$ .

$H. 7$ .

$J. 8$ .

$K. 9$ .

The answer is 20.

1 solution

Zach Abueg
Jul 19, 2017

Finding $x \ \text{mod} \ 10$ is the equivalent of the finding the last digit of $x$ . The last digit of powers of $7$ form the periodic sequence $7, 9, 3, 1$ . Hence, our answer is $7 + 9 + 3 + 1 = \boxed{20}$ .

Thank you.

Hana Wehbi - 3 years, 10 months ago

Remainder (1)

The answer is 20.

1 solution

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