AMC10 2016 B

AMC10 2016 B · Q8

AMC10 2016 B · Q8. It mainly tests Base representation, Powers & residues.

What is the tens digit of $2015^{2016}-2017$?

$2015^{2016}-2017$ 的十位数字是多少？

(A) 0 0

(B) 1 1

(D) 5 5

(E) 8 8

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Positive even powers of numbers ending in 5 end in 25. The tens digit of the difference is the tens digit of $25 - 17 = 08$, or 0.

答案（A）：以 5 结尾的数的正偶次幂都以 25 结尾。该差的十位数字等于 $25 - 17 = 08$ 的十位数字，即 0。

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