1729 (number)

1.729 ( thousand seven hundred and twenty-nine ) is the Entier naturalness which follows 1728 and precedes 1730.

Properties

Number of Hardy-Ramanujan

: 1729 are also known under the name of “number of Hardy-Ramanujan”; it is about smallest the Entier naturalness being written in two different ways like summons of two cubic S:

$1729\; =\; 12^3+1^3\; =\; 10^3+9^3$

It is thus about the Nombre taxicab of order 2.

The property of: 1729 as its name to an anecdote reported by the British Mathématicien Godfrey Harold Hardy after a visit with his/her Indian colleague is related hospitalized Srinivasa Ramanujan, in 1917:

“I remember once where I arrived at his bedside at Putney. I had been led by the taxi number: 1729; the moroseness which seemed to emanate from this number had drawn my attention. I hoped that it did not constitute ill omen. " Not, he, it answered me is an extremely interesting number; it is smallest which one can express like summons of two cubes in two manners différentes." ”

There exist natural entireties smaller than: 1729 being able to be written in two different ways like summon of two relative whole cubes of , like 91 or 189: $189\; =\; 6^3+\; \backslash \; left\; (-\; 3\; \backslash \; right)\; ^3\; =\; 4^3+5^3$ and $91\; =\; 6^3+\; \backslash \; left\; (-\; 5\; \backslash \; right)\; ^3\; =\; 4^3+3^3$.

Other properties

1.729 is also:

• the third Number of Carmichaël, i.e. a number Pseudo-first checking the property of the Small theorem of Fermat.
• a Number Harshad in bases 8,10 and 16, i.e. divisible by the sum of its figures:
• : $1729\; =\; 91\; \backslash \; times\; \backslash \; left\; (1\; +\; 7\; +\; 2\; +\; 9\; \backslash \; right)$
• a Nombre of Zeisel, i.e. its factors first are at least three and follow a arithmético-geometrical Progression (here, a Arithmetic progression of reason 6):
• : $1729\; =\; 7\; \backslash \; times\; 13\; \backslash \; times\; 19$
• a Number polygonal, more precisely dodecagonal, 24-gonal, and 84-gonal.

See too

• quoted Characters:
• Godfrey Harold Hardy
• Srinivasa Ramanujan
• remarkable Properties:
• Number taxicab
• Number of Carmichaël
• Number Harshad
• Number of Zeisel
• polygonal Number

Random links:

Platino | Slikke | Akinfiy Demidoff | Wilham of Waddington | The Ex (film, 2007) | Olivier Gouez | Robert_Adam

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