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It is proved that the sequence $[n^{c}] (n = 1, 2, \dots)$ contains infinite squarefree integers whenever $1 < c < \frac{61}{36} = 1.6944 \dots$ , which improves Rieger’s earlier range $1 < c < 1.5$ .

The distribution of squarefull numbers in short intervals

Michael Filaseta, Ognian Trifonov (1994)

Acta Arithmetica

The distribution of the values of a rational function modulo a big prime

Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

Given a large prime number $p$ and a rational function $r (X)$ defined over $𝔽_{p} = ℤ / p ℤ$ , we investigate the size of the set $\{x \in 𝔽_{p} : \tilde{r} (x) > \tilde{r} (x + 1)$ , where $\tilde{r} (x)$ and $\tilde{r} (x + 1)$ denote the least positive representatives of $r (x)$ and $r (x + 1)$ in $ℤ$ modulo $p ℤ$ .

We investigate the average order of the divisor function at values of binary cubic forms that are reducible over $ℚ$ and discuss some applications.

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Displaying 41 – 60 of 164

The distribution of Kummer sums at prime arguments.

The distribution of power residues and certain related results

The Distribution of Powerful Integers of Type 4.

The distribution of powerful integers of type 4

The distribution of primes satisfying the condition $a^{p - 1} \equiv 1 (m o d p^{2})$

The distribution of sequences in arithmetic progressions

The distribution of squarefree numbers.

The distribution of square-free numbers

The distribution of square-free numbers of the form $[n^{c}]$

The distribution of squarefull numbers in short intervals

The distribution of the values of a rational function modulo a big prime

The distribution of totients.

The Distribution Of Values Of Some Multicaptive Functions

The distribution of values of the Euler function

The divisor function $d_{3} (n)$ in arithmetic progressions

The divisor function on residue classes I

The divisor function over arithmetic progressions

The divisor problem for arithmetic progressions

The divisor problem for arithmetic progressions with small modulus

The divisor problem for binary cubic forms

Currently displaying 41 – 60 of 164