Lessons in number theory:

1) How many ordered pairs (a,b) of natural numbers have 17640 as their LCM?

2) The set of natural numbers {a1,a2,a3,...,an} is called a partition of 'N' if a1+a2+a3+...+an=N.

Consider all the partitions of N=176. There is a partition with the maximum product among all the partitions.

What's this maximum product?

P.S: don't Google these questions.

38 comments:

  1. guntashFebruary 8, 2011 at 8:27 PM

    276 and (44)^4

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  2. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 8, 2011 at 8:38 PM

    This comment has been removed by the author.

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  3. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 8, 2011 at 8:39 PM

    This comment has been removed by the author.

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  4. guntashFebruary 8, 2011 at 9:14 PM

    edit:it shud be 4^44 for 2nd ques

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  5. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 8, 2011 at 9:17 PM

    I think For second question

    (2)^88

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  6. AnonymousFebruary 8, 2011 at 10:37 PM

    1.I got 85, though I think definitely I have dn some mistake. method is x1+x2+x+x4+x5=8 now do by particular permutation and combination method. By finding range of these factors=2,3,5,7 x5 is extra which would make sum as 8.

    2.yes 2^88 or 4^44-one and the same thing

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  7. AnujFebruary 9, 2011 at 12:21 AM

    no and no.

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  8. ShivankerFebruary 9, 2011 at 12:22 AM

    m getting 263 "unordered pairs" of natural numbers for d first one for sure..

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  9. ShivankerFebruary 9, 2011 at 12:31 AM

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  10. ShivankerFebruary 9, 2011 at 12:53 AM

    the second one should be 2*3^58 i guess..

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  11. AnonymousFebruary 9, 2011 at 11:32 AM

    1.12

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  12. AnonymousFebruary 9, 2011 at 11:34 AM

    bhaiya please tell, if my approach to first question was incorrect. Because that's how we found no.s which can be formed from the given no.

    Also I forgot to take ordered pair, so it should be 85C2

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  13. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 9, 2011 at 11:46 AM

    I got the answer of the Answer of the second problem.I think so.I am getting 2 * 3^58.

    Please bhaiya tell am i right??

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  14. AnonymousFebruary 9, 2011 at 11:53 AM

    to second question also, now I am getting somewhat feel.
    Apply AM >= GM
    product >= (176)^n

    now I couldn't solve so, googled it :p, got it now. :)really good question

    to first question, I have attempted it myself(that is why it is wrong)

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  15. AnonymousFebruary 9, 2011 at 11:54 AM

    @♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○ ,
    no, its incorrect

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  16. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 9, 2011 at 12:05 PM

    No i am correct.

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  17. akash rupelaFebruary 9, 2011 at 12:43 PM

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  18. akash rupelaFebruary 9, 2011 at 12:46 PM

    it should be 505 for 1st one right?

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  19. ShivankerFebruary 9, 2011 at 12:51 PM

    first one is 525 ordered pairs akash.. : confirmed

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  20. akash rupelaFebruary 9, 2011 at 12:52 PM

    and for 2nd one i agree with 2*3^58

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  21. akash rupelaFebruary 9, 2011 at 12:53 PM

    yeah i m sorry, mismultiplied 21 and 25 :P

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  22. AnonymousFebruary 9, 2011 at 1:27 PM

    for second one as I found on internet is e^(176/e)

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  23. ShivankerFebruary 9, 2011 at 2:41 PM

    Mr. Anonymous:

    think urself.. is e a natural number??
    or is 176/e a natural number??

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  24. ShivankerFebruary 9, 2011 at 2:42 PM

    This comment has been removed by a blog administrator.

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  25. ShivankerFebruary 9, 2011 at 2:51 PM

    hey.. can anyone find the number of partitions of a natural number n???

    m trying bt cudn't get it by now.. :-/

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  26. ♥◘○µ╦┬░Γ╪╬└↑φΦ╫╛◙«½╣↔⌐☺♠♦♣◘○February 9, 2011 at 3:22 PM

    Yes i am very happy because i won question 2 competition.I stood first♣♣♠

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  27. akash rupelaFebruary 9, 2011 at 3:28 PM

    This comment has been removed by a blog administrator.

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  28. ShivankerFebruary 9, 2011 at 3:53 PM

    ok..

    thnx akash.. u're right..

    i found this creapy thing by the way lately..
    http://en.wikipedia.org/wiki/Partition_(number_theory)#Partition_function

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  29. AnonymousFebruary 9, 2011 at 4:55 PM

    This comment has been removed by a blog administrator.

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  30. AnujFebruary 9, 2011 at 5:28 PM

    I got to do some censorship..

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  31. ShivankerFebruary 9, 2011 at 5:49 PM

    sorry bhaiya..

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  32. AnujFebruary 9, 2011 at 6:28 PM

    As for the number of partitions of a natural number 'n', this was a question in our CSL105 major. I can't remember the soln. now.

    Maybe someday, we'll have a piece of that too!

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  33. akash rupelaFebruary 9, 2011 at 7:23 PM

    that would be fun

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  34. AnonymousFebruary 9, 2011 at 9:46 PM

    This comment has been removed by a blog administrator.

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  35. AnujFebruary 9, 2011 at 11:19 PM

    lets talk 'academic' stuff here...we have ole' facebook for our er...personal matters..

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  36. AnonymousFebruary 14, 2011 at 9:59 PM

    how do we get answer of first one?????????

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  37. AnonymousFebruary 14, 2011 at 10:02 PM

    is answer of 1st 525???

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  38. AnonymousFebruary 15, 2011 at 10:57 PM

    blah blah

    ReplyDelete

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