RAMANUJAN TRIPLES

A number that can be written as the sum of cubes of a number in three ways.

This is also known as TAXICAB 3

DR RAJESH KUMAR THAKUR

Ramanujan Number

Ramanujan was fond of numbers. Prof Hardy once visited the hospital to see the ailing Ramanujan riding on a taxi. The taxi number was 1729. This 1729 is called the Ramanujan Number.

C P Show in his book wrote -
“Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxicab number. Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxicab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’”

a^ 3 + b^ 3 = x where x is the Ramanujan Number

This number is also known as TAXI CAB number.

Thanks for reading

Dr Rajesh Kumar Thakur