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Hardy-Ramanujan number 1729 is famous because it is the smallest positive integer expressible as the sum of two cubes in two different ways. The two pairs are:
A6³ + 7³ and 9³ + 10³
B1³ + 12³ and 9³ + 10³
C2³ + 12³ and 5³ + 11³
D1³ + 12³ and 6³ + 13³
Answer & Solution
Correct answer: B. 1³ + 12³ and 9³ + 10³
1729 = 1 + 1728 = 1³ + 12³, and also 1729 = 1000 + 729 = 10³ + 9³. The story of Hardy visiting Ramanujan in a taxi numbered 1729 is one of the most famous anecdotes in mathematics.
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