1 citations · 3 across the 10 of their papers we have counts for
13 papers
M-Plan: Comprehensive Planning For LLM Agents with Memory Arrangement
Ziyang Liu, Jiakang Yuan, Jiayuan Fan +1
Large language model (LLM)-based agents have recently demonstrated outstanding performance in single-turn tasks, yet they continue to struggle with long-horizon tasks, particularly…
On the nonnegative integer solutions to the equation
Sagar Mandal
The Diophantine equation where denotes the -th Fibonacci number and , has attracted attention in recent years. The cases $(…
On common values of and Nathanson's totient function
Sagar Mandal
In a recent paper, Chatterjee, the author and Mohan posed the problem of determining all solutions of the Diophantine equation , where is the -th Fibonacci numbe…
On transcendence of non-periodic continued fractions associated with modular forms and arithmetic functions
Tapas Chatterjee, Sagar Mandal
The purpose of this article is two-folds. Firstly, we establish two sufficient conditions under which the sequence is non-periodic, where is an ar…
Exact and Asymptotic Counts of MSTD, MDTS, and Balanced Sets in Dicyclic Groups
Sagar Mandal, Neetu
We investigate the relationship between the sizes of the sum and difference sets of the Dicyclic Group . We first determine the exact numbers of MSTD (more sums…
Divisibility and Sequence Properties of and
Sagar Mandal
Inspired by Lehmer's and Deaconescu's conjectures, as well as various analogue problems concerning Euler's totient function , Schemmel's totient function , Jordan t…
A Note on Deaconescu's Conjecture
Sagar Mandal
Hasanalizade [1] studied Deaconescu's conjecture for positive composite integer . A positive composite integer is said to be a Deaconescu number if .…
Exploring the Relationships Between the Divisors of Friends of
Sagar Mandal
A solitary number is a positive integer that shares its abundancy index only with itself. is the smallest positive integer suspected to be solitary, but no proof has been esta…
A note on solitary numbers
Sagar Mandal
Does have a friend? Until now, this has been an open question. In this note, we prove that a potential friend of is an odd, non-square positive integer. appears i…
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…
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 $…
Upper bounds for the prime divisors of friends of 10
Sourav Mandal, Sagar Mandal
In this paper we propose necessary upper bounds for the second, third and fourth smallest prime divisors of friends of 10 based on the number of distinct prime divisors of it.
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…