One thousand seven hundred twenty-nine

This article deals with the number "1729". For the year 1729 AD see 1729 .

One thousand seven hundred twenty-nine
1729
presentation
Roman	M DCCXXIX
dual	110 1100 0001
Octal	3301
Duodecimal	1001
Hexadecimal	6C1
Morse code	- - - - - - · · · · · - - - - - - - ·
Mathematical properties
sign	positive
parity	odd
Factorization	${\displaystyle 7\cdot 13\cdot 19}$
Divider	1, 7, 13, 19, 91, 133, 247, 1729

Special features of the number 1729

Hardy Ramanujan number

The number 1729 is also known as the Hardy Ramanujan number . It is the smallest natural number for which there are exactly two representations as the sum of two positive cubic numbers .

${\displaystyle 9^{3}+10^{3}=1729}$

${\displaystyle 1^{3}+12^{3}=1729}$

Numbers with this property are called taxicab numbers . The names Hardy Ramanujan number and Taxicab number refer to an anecdote according to which the mathematician S. Ramanujan is said to have made his mentor Godfrey H. Hardy aware that the number of the taxi he used on that day was a special number be.

See also : Interesting Numbers Paradox

Sphenic number

${\displaystyle 1729=7\cdot 13\cdot 19}$is the product of exactly three different prime numbers and thus a sphenic number . The factors are the three smallest happy prime numbers .

Carmichael number

1729 is a Carmichael number , because for all bases that do not have a prime factor in common with 1729 (1729 = 7 13 19): ${\displaystyle a}$

${\displaystyle a^{1728}\equiv 1\quad ({\rm {mod\ }}1729)}$

It is the smallest Carmichael number constructed according to the Chernick method , i.e. the smallest Carmichael number in the form

${\displaystyle 1296k^{3}+396k^{2}+36k+1}$

Harshad number

The 1729 is also a Harshad number , which means that it is divisible by the sum of its digits:

${\displaystyle 1729=(1+7+2+9)\cdot 91}$

literature

• Robert Kanigel: Who knew the infinite. The life of the brilliant mathematician Srinivasa Ramanujan . 2nd Edition. Vieweg, Braunschweig et al. 1995, ISBN 3-528-06509-5 , p. 276.
• Michael Köhlmeier : Occident. Roman, 3rd edition, Deutscher Taschenbuchverlag, Munich 2009, ISBN 978-3-423-13718-8 , p. 611 .

Individual evidence

1. ↑ Simon Singh : Homer's last sentence: The Simpsons and the Mathematics , page 242, Hanser, Munich 2013, ISBN 978-3-446-43771-5