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Find the number which can be written as a^3+b^3 and c^3+d^3,where a,b,c,d are distinct and belongs to natural numbers.Note:-The number is not Ramanujan Number.

Find the number which can be written as a^3+b^3 and c^3+d^3,where a,b,c,d are distinct and belongs to natural numbers.Note:-The number is not Ramanujan Number.

Grade:10

2 Answers

aneesh reddy
17 Points
8 years ago

That''s good question.....13832 this number can be written as 18^3+20^3 and 24^3 + 2^3..

Adhiraj Mandal
32 Points
8 years ago

Yes it is a good question but the solution is tricky

The RAMANUJAN NUMBER is 1729=1^3+12^3=10^3+9^3

Multiply this number by any perfect cube ,say k^3

Then k^3(1729)=k^3(1^3+12^3)=k^3(10^3+9^3)

which can be written as [k^3+(12k)^3]=[(10k)^3+(9k)^3]=1729k^3

EXAMPLE:Take k=11

             Then the required number is 1729*1331=2301299=11^3+132^3=110^3+99^3

      ANY SUCH VALUE FOR k WILLDO THE TRICK 

I think I have passed your test.Wink

With regards ADHIRAJ

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