1729 (number)

[a] Furthermore, it is the first in the family of absolute Euler pseudoprimes, a subset of Carmichael numbers.

[7] 1729 is divisible by 19, the sum of its digits, making it a harshad number in base 10.

[8] 1729 is the dimension of the Fourier transform on which the fastest known algorithm for multiplying two numbers is based.

Investigating pairs of its distinct integer-valued that represent every integer the same number of times, Schiemann found that such quadratic forms must be in four or more variables, and the least possible discriminant of a four-variable pair is 1729.

1729 is also known as Ramanujan number or Hardy–Ramanujan number, named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan who was ill in a hospital.

[16] This conversation led to the definition of the taxicab number as the smallest integer that can be expressed as a sum of two positive cubes in distinct ways.

[15] 1729 was later found in one of Ramanujan's notebooks dated years before the incident, and it was noted by French mathematician Frénicle de Bessy in 1657.

[17] A commemorative plaque now appears at the site of the Ramanujan–Hardy incident, at 2 Colinette Road in Putney.