Taxicab number Ta(n): smallest number expressible as sum of two positive cubes in n distinct ways. Ta(1)=2=1³+1³. Ta(2)=1729=1³+12³=9³+10³ (Hardy-Ramanujan number). The name comes from Ramanujan's famous taxi ride story.
How to Use
Features:
- Check: Find cube sum representations
- Ta(n): Known taxicab numbers
- Search: Numbers with multiple representations
The 1729 Story
G.H. Hardy visited Ramanujan in hospital, mentioning his taxi was number 1729 — 'a rather dull number.' Ramanujan instantly replied: 'No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'
Known Values
- Ta(1) = 2 = 1³+1³
- Ta(2) = 1729 = 1³+12³ = 9³+10³
- Ta(3) = 87539319
- Ta(4) = 6963472309248
- Ta(5) = 48988659276962496
Step-by-Step Instructions
- 1Enter a number.
- 2Find cube representations.
- 3Check if taxicab.
- 4View known Ta(n).
- 5Search range.