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Omni-MATH / G.H. Hardy once went to visit Srinivasa Ramanujan in the hospital, and he…

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problem

G.H. Hardy once went to visit Srinivasa Ramanujan in the hospital, and he started the conversation with: "I came here in taxi-cab number 1729. That number seems dull to me, which I hope isn't a bad omen." "Nonsense," said Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." Ramanujan had immediately seen that 1729=123+13=103+931729 = 12^{3} + 1^{3} = 10^{3} + 9^{3}. What is the smallest positive integer representable as the sum of the cubes of three positive integers in two different ways?
Plain-text mathematical notation (without MathML)
G.H. Hardy once went to visit Srinivasa Ramanujan in the hospital, and he started the conversation with: "I came here in taxi-cab number 1729. That number seems dull to me, which I hope isn't a bad omen." "Nonsense," said Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." Ramanujan had immediately seen that 1729=12³+1³=10³+9³. What is the smallest positive integer representable as the sum of the cubes of three positive integers in two different ways?
Original LaTeX notation
G.H. Hardy once went to visit Srinivasa Ramanujan in the hospital, and he started the conversation with: "I came here in taxi-cab number 1729. That number seems dull to me, which I hope isn't a bad omen." "Nonsense," said Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." Ramanujan had immediately seen that $1729 = 12^{3} + 1^{3} = 10^{3} + 9^{3}$. What is the smallest positive integer representable as the sum of the cubes of three positive integers in two different ways?

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task_id
56cb8ede-214f-5817-b1f2-3ad983d06402
task_key
test--56cb8ede-214f-5817-b1f2-3ad983d06402
task_revision_id
1
config / split
/ test

Official source

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