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if [x] denotes greatest integer < or = x ,
then prove that
C(n,3)  [ n/3 ]
is a natural no. , divisible by 3 for all integer n> or =3
 one year ago
 one year ago
if [x] denotes greatest integer < or = x , then prove that C(n,3)  [ n/3 ] is a natural no. , divisible by 3 for all integer n> or =3
 one year ago
 one year ago

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shubhamsrgBest ResponseYou've already chosen the best response.0
C(n,3) here denotes comination, for e.g. C(4,3) = 4! / (43)! (3)! likewise..
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1345190132115:dwdw:1345190209186:dw n can have only 3 from ... 1) 3k 2) 3k+1 3) 3k+2
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
am all years..what next ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
lol..i meant "ears"
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1345190372362:dw this is just a try man ... i never know the solution beforehand.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
that 4 wont be there in the last step...anyways nice... it'll be always divisible by sine its 9*something..and one of k and k1 is always even so the 2 cancelled out..thus 3k satisfies it.. nice..
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i meant it'll always be divisible by 3**
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
lol ... how ... you always need k of the form to be k, k  1, k  2
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Oh ... sorry ... such a huge error!! :(((
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
same thing repeats in other cases .. since you have three terms of m, m+1, m+2 < one of them is going to be divisible by 3
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
and that [n/3] thing is not going to change.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
excellent,,thans a lot :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
not really ... i guess i should get some more sleep :)
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
yeah you must be tired..go and relax..even very sharp minds need sound sleep! ;)
 one year ago
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