Problem 9:
Sum of three positive integers is $2^{2011} + 1$, and the product of two of them is $2^{2011}$. How many values can the third integer take?
Rangpur Higher Secondary 2011/9
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Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.

 Posts: 78
 Joined: Thu Jan 20, 2011 10:46 am
Re: Rangpur Higher Secondary 2011/9
Let XY=2^2011&X+Y+Z=2^2011+1.Now think of how many ways we can makeXY.The result should be 1005
Re: Rangpur Higher Secondary 2011/9
third integer will be odd. how did you get your ans...?
Try not to become a man of success but rather to become a man of value.Albert Einstein

 Posts: 78
 Joined: Thu Jan 20, 2011 10:46 am
Re: Rangpur Higher Secondary 2011/9
U just think about how many ways u can make XY.Then the another one is third number.What's problem if it is odd?Bcoz 2^2011+1 is odd.