Arpit Sachan

. Why 1729 is Special Number ? 1729 is the Hardy Ramanujan Number. It is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 - a cube of 10 is 1000 and a cube of 9 is 729; adding the two numbers results in 1729. 1729 is also the sum of the cubes of 12 and 1- a cube of 12 is 1728 and a cube of 1 is 1; adding the two results in 1729 Such as -      1729 = 1000 + 729 = (10)³ + (9)³     1729 = 1728 + 1 = (12)³ + 1³ It is also incidentally product of three prime numbers, As-      1729 = 7 X 13 X 19