2025/06/26 by Mandal, Sagar · 1 citation
#11A25 #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2507.02930
Hasanalizade [1] studied Deaconescu's conjecture for positive composite integer n. A positive composite integer n≥4 is said to be a Deaconescu number if S2(n)| ϕ(n)-1. In this paper, we improve Hasanalizade's result by proving that a Deaconescu number n must have at least seventeen distinct prime divisors, i.e., ω(n)≥ 17 and must be strictly larger than 5.86⋅1022. Further, we prove that if any Deaconescu number n has all prime divisors greater than or equal to 11, then ω(n)≥ p*, where p* is the smallest prime divisor of n and if n∈ D3 then all the prime divisors of n must be congruent to 2 modulo 3 and ω(n)≥ 48.