Hardy-Ramanujan Number for ^2's

Number Theory Level 2

The Hardy-Ramanujan Number is a number that can be expressed in the form of 2 cubic numbers in 2 ways. 1729 is the smallest Hardy-Ramanujan Number , as; 1729=10^3+9^3; 12^3+1^3 . Find the smallest number for square numbers. (in the form of- x=y^2+z^2;a^2+b^2)


The answer is 85.

Pinaki Biswas by Pinaki Biswas , 45, India

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1 solution

Pinaki Biswas
Oct 4, 2018

125=10^2+5^2;11^2+2^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

how about 50 = 5 2 + 5 2 ; 1 2 + 7 2 50 = 5^2+5^2; 1^2+7^2 ? To exclude this, you should specify that x ≠ y x \ne y and a ≠ b a \ne b .

How about 85 = 2 2 + 9 2 ; 6 2 + 7 2 85=2^2+9^2;6^2+7^2

Laszlo Mihaly - 2 years, 8 months ago

And how about 65 = 1 2 + 8 2 = 4 2 + 7 2 65 = 1^2 + 8^2 = 4^2 + 7^2 ?

You need to specify why 50 , 65 , 85 50, 65, 85 are not correct answers.

Michael Mendrin - 2 years, 8 months ago

1 pending report

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