Nikhil S Kumar

collaborators

2 papers

math.NT2025

How often are $⌊ n^{α} ⌋$ and $⌊ n^{β} ⌋$ simultaneously primes?

Anup B. Dixit, Nikhil S Kumar

Let $⌊ x ⌋$ denote the greatest integer less than or equal to a real number $x$ . Given real numbers $0 < α_{1} < α_{2} < \dots < α_{k} < 1$ satisfying a certain condition,…

math.NT2024

Mahler's $\frac{3}{2}$ problem in $Z^{+}$

Nikhil S Kumar

This problem was asked to K. Mahler by one of his Japanese colleagues, a Z-number is a positive real number $x$ such that the fractional parts of $x (\frac{3}{2})^{n}$ are less than…

How often are ⌊nα⌋ and ⌊nβ⌋ simultaneously primes?

Mahler's 23​ problem in Z+

How often are $⌊ n^{α} ⌋$ and $⌊ n^{β} ⌋$ simultaneously primes?

Mahler's $\frac{3}{2}$ problem in $Z^{+}$