Which of the following numbers is not a Hardy -
Ramanujan number?
(1) 4104 (2) 13832
(3) 1729 (4) 6859
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I think you did mistake in typing. here question should be ---> Which of the following numbers is a Hardy -
Ramanujan number ?
(1) 4104 (2) 13832
(3) 1729 (4) 6859
solution : 1729 is known as Hardy - Ramanujan number. actually, a very interesting story behind this number. one day, famous mathematician Ramanujan was ill and his friend hardy (mathematician) comes to meet him. and Ramanujan ask him about the taxi number. Hardy said " there was a boring number 1729" . Ramanujan said " 1729 is not a boring number. it is the smallest number which gives two pair sum of cubes of two different numbers " .
1729 = 1³ + 12³ , hence it is sum of cubes of 1 and 12
1729 = 10³ + 9³ , hence , it is also sum of cubes of 10 and 9.
after that, 1729 is known as Hardy - Ramanujan number.
hence, option (3) is correct
Ramanujan number ?
(1) 4104 (2) 13832
(3) 1729 (4) 6859
solution : 1729 is known as Hardy - Ramanujan number. actually, a very interesting story behind this number. one day, famous mathematician Ramanujan was ill and his friend hardy (mathematician) comes to meet him. and Ramanujan ask him about the taxi number. Hardy said " there was a boring number 1729" . Ramanujan said " 1729 is not a boring number. it is the smallest number which gives two pair sum of cubes of two different numbers " .
1729 = 1³ + 12³ , hence it is sum of cubes of 1 and 12
1729 = 10³ + 9³ , hence , it is also sum of cubes of 10 and 9.
after that, 1729 is known as Hardy - Ramanujan number.
hence, option (3) is correct
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