Talk:999 (number)

Number 999 may also be considered as a 'taxicab number', defined according to the famous Indian mathematician Ramanujan, except that it is equal not to the sum, but to the difference of two perfect cubes, in two different ways:

      a) 999 = 1000 - 1  = 10^3 - 1^3
      b) 999 = 1728 - 729  = 12^3 - 9^3

Beside this example, there must certainly exist other numbers like this, that are each equal to the difference of two cubes in 3, 4,...n different ways.

Kaprekar number

The number 999 is indeed a Kaprekar number in base-10.

However, the article points this out as so:

999 = 3³ × 37, a Kaprekar number.

To me, this seems like a non-sequitur; I fail to understand how the prime factorization of 999 relates to the property of it being a Kaprekar number. Wouldn't it make sense to instead write "999² = 998001 = (998 + 001)², so 999 is a Kaprekar number", or something along those lines? Maybe I'm failing to realize something about how prime factorization relates to this property. 152.3.43.55 (talk) 16:44, 5 December 2022 (UTC)