Question

Write the last digit of fifth power of 345678.

Answer 1

Answer:

.Many mathematical contests ask students to find the last digit (or digits) of a power. In most cases, the powers are quite large numbers such as 6032^{31}6032

31

or 89^{47},89

47

, so that computing the power itself is out of the question.

However, there are a number of tools, such as modular arithmetic, the Chinese remainder theorem, and Euler's theorem that serve as shortcuts to finding the last digits of an expanded power. Solving these types of problems gives a down-to-earth introduction to these techniques of elementary number theory