11is it 1729?
13 + 123 = 1729
93 + 103 = 1729
just a try :)
Just like 2 is the smallest natural number which can be represented a sum of two cubes in one way.
i.e. - 2 = 13 + 13
Find the smallest natural number representable in two different ways as a sum of two cubes.
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8 Answers
71It was given by Ramanujan while he was to die.!!!. Really What a great man he was!
11The number derives its name from the following story G. H. Hardy told about Ramanujan.
"Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought
about it a little because he entered the room where Ramanujan lay in bed and, with scarcely
a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,'
adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, 'it is a very
interesting number. It is the smallest number expressible as the sum of two [positive] cubes
in two different ways' "
71Ohh! No one giving importance to my Story!! . It was more good! :P
11People haven't yet found a no. which can be written as a sum of two numbers each to the power 5 in 2 ways.
i.e.:
a5+b5=c5+d5=x
The haven't yet found a single value for x.
11arey they have left something for us to prove and discover, sab kuchh wohi log kar jate toh
hum kya karte?
@ Shaswata you search some number which can be written as a sum of two numbers each
to the power 5 in 2 ways.
Wish you all the best :)
1@shaswata it has been found out see down for such values
a=k
b=-k
c=m
d=-m
and u can keep any integral values for k,m......such as -2,-4,4,5,6,67..........