Was Ramanujan Right??!
Once,Ramanujan found a number,he said that it is the least positive integer that can be expressed as a sum of two different cubes in two different ways.
Find this number.
Please share if u like it.
The answer is 1729.
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3 solutions
Yes i read this in my 8 class
and that mathematician was G.H. hardy and hence this number was named as hardy - ramanujan number also!
1729 is the smallest number which can be expressed as the sum of cubes of two different pairs of numbers (12,1 and 9,10).One should remember that 1729 is one of the Hardy Ramanujan numbers.
It is not the only number which can be expressed in such a way
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Can you name some ?
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You can just "make" more: Let n be a number which can be expressed in such a way.Then: n = a 3 + b 3 = c 3 + d 3 Multiplying both sides by k 3 ,where k is any positive integer,we get: k 3 n = ( k a ) 3 + ( k b ) 3 = ( k c ) 3 + ( k d ) 3 Hence,if n is a number which can be expressed in such a way,than k 3 n can also be expressed in such a way.
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@Abdur Rehman Zahid – Did you read the solution properly ?
I mentioned that 1729 is the smallest number which can be represented in such a way.
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@Rama Devi – I'm sure that I did.
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@Abdur Rehman Zahid – I seriously think that there was 'only' instead of 'smallest' there. However,if I am wrong,then sorry
The number is 1729.....
It can be expressed as,
1^3+12^3=1729
9^3+10^3=1729.
It is 1 7 2 9 , also known as the Ramanujam Number. When a mathematician came to visit him when he was sick, he accidentally told Ramanujam that the taxi he came in was unlucky, because it had 1 7 2 9 . Ramanujam almost instantly replied that it was lucky, because
1 7 2 9 = 1 0 3 + 9 3 = 1 2 3 + 1 3 .
Hats off, Ramanujam.