30 citations · 30 across the 9 of their papers we have counts for
6 papers · 1 filter
The series that Ramanujan misunderstood
Geoffrey B Campbell, Aleksander Zujev
We give a new appraisal of a famous oscillating power series considered by Hardy and Ramanujan related to the erroneous theory of distribution of primes by Ramanujan.
On integer solutions to x^5 - (x+1)^5 -(x+2)^5 +(x+3)^5 = 5^m + 5^n
Geoffrey B Campbell, Aleksander Zujev
We give an infinite number of integer solutions to the Diophantine equation x^5 - (x+1)^5 -(x+2)^5 +(x+3)^5 = 5^m + 5^n, and some solutions to some similar equations.
Some equations with features of digit reversal and powers
Geoffrey B. Campbell, Aleksander Zujev
In this paper we consider integers in base 10 like , where , , are digits of the integer, such that , where is a positiv…
Gaussian integer solutions for the fifth power taxicab number problem
Geoffrey B Campbell, Aleksander Zujev
The famous open problem of finding positive integer solutions to is considered, and related solutions are found in two distinct settings: firstly, where …
Variations on Ramanujan's nested radicals
Geoffrey B Campbell, Aleksander Zujev
We give new nested radical equations of similar kind to Ramanujan's questions to the Indian Mathematical Society 100 years ago. While many have since considered these from the pers…
A diophantine sum with factorials
Geoffrey B. Campbell, Aleksander Zujev
We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher…