Question

1. 1729 can be expressed as sum of cubes of two numbers 1729 = 13 + 123 and 93 + 103
a. Find 2 more such numbers that can be expressed as sum of cubes of natural numbers
b. What special name is given to the number 1729?

Answer 1

Solution -

The number 1729 has several special properties .

Those properties include that it can be expressed as a sum of cubes in two different ways .

For example -

1729 can be written as -

=> 1000 + 729

=> ( 10 )³ + ( 9 )³

This number , 1729 can be also written as -

=> 1728 + 1

=> ( 12 )³ + ( 1 )³

Now ,

Another number that can be expressed as sum of cubes of natural numbers is 4010.

This is however difficult to spot as it is difficult to spot two digit cubes.

For example ,

4010 can be written as 4096 + 8

This is actually , ( 16 )³ + ( 2)³

4010 can also be written as -

=> 3375 + 729

This is actually , ( 15 )³ + ( 9)³

Another such number is 13832 .

These special numbers are also known as Ramanujan - Hardy Numbers.

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Answer 2

here is the answer

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