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Subject: "Number Theory Problem"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #406
Reading Topic #406
shivgaur
Member since Mar-9-11
Mar-09-11, 09:58 AM (EST)
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"Number Theory Problem"
 
   The question is:

Show that there are positive integers m and n, with m > n, such that 2^m – 2^n is a multiple of 2011.
You do not need to find particular values of m and n, but just show that they exist.

Any lines of attack for this problem?

Shiv


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alexb
Charter Member
2780 posts
Mar-09-11, 10:02 AM (EST)
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1. "RE: Number Theory Problem"
In response to message #0
 
   Have a look at

https://www.cut-the-knot.org/pigeonhole/powers.shtml


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shivgaur
Member since Mar-9-11
Mar-13-11, 03:56 PM (EST)
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2. "RE: Number Theory Problem"
In response to message #1
 
   Thanks Alex. Will it a go!

Shiv


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