Daffodil International University

Educational => Mathematics => Problems and Solutions => Topic started by: msu_math on November 12, 2012, 12:50:28 PM

Title: Challenging Problem: Computing digits of numbers with integer powers
Post by: msu_math on November 12, 2012, 12:50:28 PM

Compute the last 3 digits of the number 171¹⁷².

Title: Re: Challenging Problem: Computing digits of numbers with integer powers
Post by: msu_math on November 14, 2012, 09:54:27 AM

The last digit of 171¹⁷² is obviously 1. But finding the other two digits, of course, a difficult task. Since the number 171¹⁷² consists of a lot of digits, expanding it directly by using calculator/computer is almost impossible and hand calculation is so tough and lengthy. However, we must recall some theorems and formulas to solve this problem.