# Tag Archives: Ramanujan

## Two squares that sum to a cube

Introduction This note records an exploration that began in our youth with the simple arithmetic question: Sum of the squares of which pair integers yields a perfect cube? Some obvious cases immediately come to mind: . In both these cases … Continue reading

## The quotient triangle, the parabola-hyperbola sequence, the remainder triangle and perfect numbers

The quotient triangle Consider a positive integer . Then for all do the floor operation . Say , we get , a sequence of quotients of the division . If we do this for all we get the quotient triangular … Continue reading

## Counting primes, arithmetic functions, Ramanujan and the like

We originally wished to have a tail-piece for our previous note that would describe more precisely the relationship between the Möbius function and the distribution of prime numbers. However, since that would have needed a bit of a detour in … Continue reading

## Of lives of men; of times of men-II

Of lives of men; of times of men-I Vidrum: “When we attended the discussions at the Right Wing Debate club we heard the president Rammandir Mishra repeatedly emphasize that South Asian civilization was not a ‘history-centric’ civilization and that history-centricism … Continue reading

## The magic of the deva-ogdoad

Classical Hindu tradition holds that the ogdoad of deva-s corresponding to their directions is: Indra: East; Agni: Southeast; Yama: South; Nirṛti: Southwest; Varuṇa: West; Vāyu: Northwest; Kubera: North; Īśāna: Northeast. The central position might be occupied in certain traditions by … Continue reading

## Euler and Ramanujan: primes, near integers and cakravāla

Mathematician Watson who worked on the famed notebooks said regarding some of Srinivasa Ramanujan’s equations: “a thrill which is indistinguishable from the thrill which I feel when I enter the Sagrestia Nuovo of the Capella Medici and see before me … Continue reading