Math Olympiad Question: Sum of powers of two

Is there a number that is a sum of two powers of 2, and ends with 3 zeros?

The answer is yes!

For example, 2^3+2^{253}=14474011154664524427946373126085988481658748083205070504932198000989141205000

How about n zeroes?

Check out last month’s problem of the month at: http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem.htm

Question: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1409q.pdf

Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1410a.pdf

 


Featured book:

104 Number Theory Problems: From the Training of the USA IMO Team

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

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