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General Forum: Education | | ******MATHEMATICS****** | |
| AyanE unTE mangalendukanI, A mATram tIrAlostE nEnu lekhkhala parIkshallO enduku tapputAnU? anta mEdhassunTE ikkaDa samAdhAnAlenduku chebutArU?
Posted by: Bahud♥♥rapu Baatasaari At: 26, Apr 2004 3:10:01 PM IST
Prove that there are infinitely many integers that are not equal to the sum of two squares of integers, but that are equal to the sum of three cubes of integers.
Posted by: Raj Sekhar At: 26, Apr 2004 1:36:08 PM IST
marandukE nAku manDEdi. dInjIvitam ... if difference between consecutive integers is a perfect square ani, 8^3, 7^3 anTU kyUb enduku tIsukunTAru? nAlAnTi sAmAnya prajalekeppuDartham autundO I mEthamETriks
Posted by: Durga Prasad At: 9, Feb 2004 7:45:19 PM IST
mod 9 aithe sum of the numbers batti aa number kanukkovacchani.....
how could i miss this question....konchem clear gaa ledu question........frank,u there now?
Posted by: Raj Sekhar At: 9, Feb 2004 3:40:33 PM IST
This is a question I fould in the trivia section of a Mathematics journal ..way back in 1997. When I started attempting it ..it turned out to be a hard nutshell to crack. Luckily, I solved it.But still am not sure whether its "the" elegant solution.
Here's the problem :-)
Prove that if the difference between consecutive integers is a perfect square, then the difference can be written as the square of the sum of the squares of two other consecutive integers.
The first set of numbers to follow this are 7,8
(8)^3 - (7)^3 = 169 = (13)^2 = ( 4 + 9 )^2
4 is a perfect square and so is 9.
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Raj, it shd be cakewalk for u :-).btw can u let me knw why u used only "mod9" test...cant we use anything else ( ofcourse not 2,5,10).
Posted by: Mr. Frank Abagnale Jr. At: 18, Nov 2003 5:33:13 PM IST
aahaa....ala kaadandi...
7451/mod9 = (7+4+5+1)mod9 = 8
and 3982/mod9 = 4
hence product/mod9 = 8x4/mod9 = 5 avvaali
hence 29*69882/mod9 = 5
(2+9+*+6+9+8+8+2)/mod9 = 5
(44+*)/mod9 = 5
hence * = 6
Posted by: Raj Sekhar At: 18, Nov 2003 10:27:21 AM IST
4000-18 ila vesukuni cheyyochaa.....direct gaa cheppalaa....labham ledu meere cheppeyandi..
Posted by: Mrs. Aruna At: 18, Nov 2003 7:49:18 AM IST
7451 x 3982 = 29*69882
"*" is a missing number...
can u find out the missing number without performing the multiplication???
Posted by: Raj Sekhar At: 17, Nov 2003 11:18:49 AM IST
ohh i c......yes, even it seems like the correct solution now also .But putting down in explicti fashion rather than in abstract sense .. hits the nail in the coffin of the problem.
Posted by: Mr. Frank Abagnale Jr. At: 16, Nov 2003 11:51:53 AM IST
oohhalaanaa......i think,i cant.....actually,somebody asked someother this question,he asked me and i answered hi like this........i too dont know the actual solution.....but the original person agreed that this solution is right....
explicit gaa represent cheyyalememo......
Posted by: Raj Sekhar At: 16, Nov 2003 11:49:12 AM IST
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