In my previous blog of 18th feb,I had mentioned about the number 1729-called Ramanujan number-the only number which could be expressed as a sum of 2 cubes in 2 different ways-viz 1000+729=1728+1=1729.
If we consider differences between 2 cubes (this means the same thing as considerig the cube of one negative number),we can write the equations differently....12^3+{(-)10}^3=1729-1000=728 also 9^3+{(-1)}^3=729-1=728.
I can now show a case where a number can be expressed as a difference of 2 cubes in 3 different ways
34^3-33^3=39304-35937=3367
15^3-2^3 = 3375-8 =3367
16^3-9^3 = 4096-729=3367
There could be many more such cases.-also numbers which could be expressed in more than 3 different ways.
If we consider differences between 2 cubes (this means the same thing as considerig the cube of one negative number),we can write the equations differently....12^3+{(-)10}^3=1729-1000=728 also 9^3+{(-1)}^3=729-1=728.
I can now show a case where a number can be expressed as a difference of 2 cubes in 3 different ways
34^3-33^3=39304-35937=3367
15^3-2^3 = 3375-8 =3367
16^3-9^3 = 4096-729=3367
There could be many more such cases.-also numbers which could be expressed in more than 3 different ways.
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