When English mathematician G.H. Hardy visited Srinivasa Ramanujan in the hospital, Hardy noted that the number of his taxicab was $1729$, remarking that it seemed rather dull. Ramanujan immediately replied: "No, Hardy, it is a very interesting number! It is the smallest number expressible as the sum of two cubes in two different ways." Indeed: $$1729 = 1^3 + 12^3 = 9^3 + 10^3$$ Write a program with nested loops to check numbers from $1$ to $3{,}000$ and find the first number that can be written as $a^3 + b^3$ in two different ways ($1 \le a \le b$). Does your code find $1729$? What are the pairs $(a, b)$?See your results here: