## Rangpur Higher Secondary 2011/9

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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### Rangpur Higher Secondary 2011/9

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?

Mehfuj Zahir
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

photon
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### 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

Mehfuj Zahir
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.