Ta(2)
Number Theory
Level
4
How many ordered pairs of positive integers are there such that ?
Hint : Taxicab
6
2
4
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1 solution
1729 is the second taxicab number(1729 is also known as the Hardy-Ramanujan number) ,which means that it can be written as the sum of two cubes in two distinct ways.However,the problem states "ordered pairs of integers",so there are 4 pairs.They are ( 9 , 1 0 ) , ( 1 0 , 9 ) , ( 1 2 , 1 ) , ( 1 , 1 2 ) .