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![[Post New]](/templates/default/images/icon_minipost_new.gif) 25 Jan 2007 20:49:53 IST
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Hi, Find the number of positive integral solutions to the equation  thanks for your time.
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2 2s can occupy = 3C1*3C1 =9 positions 2 3s can occupy = 3C1*3C1 =9 positions 3 5s can occupy = 3C1*3C1*3C1 =27 positions total number of solution= 9*9*27
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26 Jan 2007 03:09:57 IST
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hello vikrant are u sure this is the ans well i think! as 2 3 5 are prime no's therefore u can use the simple formula which states that no of factors or integral soln.(if unknown like u asked) of any no. is given by (p+1)(q+1)(r+1).........where p q r are coffecients raise to the power of prime no. for eg 2^2.3^2.5^3= (2+1)(2+1)(3+1) = 3.3.4 =36 therefore 36 no. of inegral soln. are there . just tell me the ans konichiwa2x
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26 Jan 2007 12:59:48 IST
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no I dont think what you say is right. That only gives you the number of factors. number of factors and solutions are not the same. i think vikrant is correct.
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Guide to latex:
http://www.goiit.com/posts/list/community-shelf-a-guide-to-latex-48056.htm
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26 Jan 2007 13:13:20 IST
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 Yes I also agree with Vikrant's sol.
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27 Jan 2007 14:18:08 IST
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actually, now I feel what vikrant said is wrong. if you were to have:  where the p's are prime, then
each of the  's could be "distributed" among the k factors in  (ie,mj+k-1 C k-1 ) ways.
Thus the answer to problem is : 
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Guide to latex:
http://www.goiit.com/posts/list/community-shelf-a-guide-to-latex-48056.htm
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27 Jan 2007 21:48:59 IST
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exactly
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The Scientist does not study nature because it is useful; he studies it because he delights in it, & he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, life would not be worth living. Ofcourse I do not here speak of that beauty that strikes the senses, the beauty of qualities & appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmoniuos order of the parts, & which a pure intelligence can grasp. |
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