Are there other no like 1729?

Answer 1

Yes. But depending on the characteristic of 1729 that is chosen, there are different answers:

1729, the Ramanujan-Hardy number is the smallest sum of two different pairs of positive cubes. Being the smallest such number, there cannot be another LIKE it because the other won't be the smallest.

Also, if negative numbers are allowed, there is a much smaller solution:

63 + (-5)3 = 216 - 125 = 91

and

43 + 33 = 64 + 27 = 91

This can also be presented as four consecutive integers, the sum of the smaller two cubed being the same as the difference of the larger two cubed.

The 1729th decimal place is the beginning of the first occurrence of all ten digits consecutively in the decimal representation of e, the base of natural logariths. This is not unique because it would apply to e+0.5 or e plus any decimal that terminates before 1729 places, it is unique in the sense that few mathematicians will come across memorable transcendental numbers other than e and pi.

1729 is one of only 4 positive integers such that the sum of its digits multiplied by the reversal of the answer gives the original number.

This 1+7+2+9 = 19 and 19*91 = 1729. In this case, then, there are three other numbers, although one of them is trivial: it is 1.