3 papers
math.GM2025
Prime Divisors of 10's Friends: A Generalization of Prior Bounds
Sagar Mandal
10 is the smallest positive integer which is whether solitary or friendly is still an open question in mathematics. In this paper, we provide upper bounds for each of the prime div…
math.GM2025
On Characterizing Potential Friends of 20
Tapas Chatterjee, Sagar Mandal, Sourav Mandal
Does have a friend? Or is it a solitary number? A folklore conjecture asserts that has no friends i.e. it is a solitary number. In this article, we prove that, a friend $…
math.NT2025
A note on necessary conditions for a friend of 10
Tapas Chatterjee, Sagar Mandal, Sourav Mandal
Solitary numbers are shrouded with mystery. A folklore conjecture assert that 10 is a solitary number i.e. it has no friends. In this article, we establish that if is a friend…