R. Mestrovic

activity

20112026

most citedWolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)

32 citations · 54 across the 14 of their papers we have counts for

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math.NT2018

Two curious inequalities involving different means of two arguments

Romeo Meštrović, Miomir Andjić

For two positive real numbers $x$ and $y$ let $H$ , $G$ , $A$ and $Q$ be the harmonic mean, the geometric mean, the arithmetic mean and the quadratic mean of $x$ and $y$ , respectivel…

math.NT2014

A primality criterion based on a Lucas' congruence

Romeo Mestrovic

Let $p$ be a prime. In 1878 É. Lucas proved that the congruence $(k p - 1) \equiv (- 1)^{k} (mod p)$ holds for any nonnegative integer $k \in {0, 1, \dots, p - 1}$ . The converse st…

math.NT2012★ 2 cited

Variations of Lucas' Theorem Modulo Prime Powers

Romeo Mestrovic

Let $p$ be a prime, and let $k, n, m, n_{0}$ and $m_{0}$ be nonnegative integers such that $k \geq 1$ , and $_{0}$ and $m_{0}$ are both less than $p$ . K. Davis and W. Webb established that for a…

math.NT2012★ 2 cited

A search for primes $p$ such that Euler number $E_{p - 3}$ is divisible by $p$

Romeo Mestrovic

Let $p > 3$ be a prime. Euler numbers $E_{p - 3}$ first appeared in H. S. Vandiver's work (1940) in connection with the first case of Fermat Last Theorem. Vandiver proved that $x^p+y^p…

math.NT2011★ 32 cited

Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)

Romeo Mestrovic

In 1862 Wolstenholme proved that for any prime $p \geq 5$ the numerator of the fraction $1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{p - 1}$ written in reduced form is divisible by $p^{2}$ , $(…

math.NT2011★ 4 cited

An Extension of a Congruence by Kohnen

Romeo Mestrovic

Let $p > 3$ be a prime, and let $q_{p} (2) = (2^{p - 1} - 1) / p$ be the Fermat quotient of $p$ to base 2. Recently, Z. H. Sun proved that \sum_{k=1}^{p-1}\frac{1}{k\cdot 2^k}\equiv q_p(2)-\fra…

math.NT2011

Clarkson's type inequalities for positive $l_{p}$ sequences with $p \geq 2$

Romeo Mestrovic

For a fixed $1 \leq p < + \infty$ denote by $∥ \cdot ∥_{p}$ the usual norm in the space $l_{p}$ (or $L_{p}$ ). In this paper we prove that for all real numbers $p$ and $q$ such that $2\l…

math.NT2011★ 1 cited

An Extension of a Congruence by Tauraso

Romeo Mestrovic

For a positive integer $n$ let $H_{n} = \sum_{k = 1}^{n} 1/ n$ be the $n$ th harmonic number. In this note we prove that for any prime $p \geq 7$ , $$ \sum_{k=1}^{p-1}\frac{H_k}{k^2}\equiv \su…

math.NT2011★ 4 cited

Congruences for Wolstenholme primes

Romeo Mestrovic

A prime number $p$ is said to be a Wolstenholme prime if it satisfies the congruence $(p - 1 2 p - 1) \equiv 1 (mod p^{4})$ . For such a prime $p$ , we establish the expre…

math.NT2011

On the mod $p^{2}$ determination of $\sum_{k = 1}^{p - 1} H_{k} / (k \cdot 2^{k})$ : another proof of a conjecture by Sun

Romeo Mestrovic

For a positive integer $n$ let $H_{n} = \sum_{k = 1}^{n} 1/ k$ be the $n$ th harmonic number. Z. W. Sun conjectured that for any prime $p \geq 5$ , $$ \sum_{k=1}^{p-1}\frac{H_k}{k\cdot 2^k} \e…

math.NT2011

An elementary proof of a congruence by Skula and Granville

Romeo Mestrovic

Let $p \geq 5$ be a prime, and let $q_{p} (2) := (2^{p - 1} - 1) / p$ be the Fermat quotient of $p$ to base 2. The following curious congruence was conjectured by L. Skula and proved by A. Gran…

math.NT2011

On the mod $p^{7}$ determination of $(p - 1 2 p - 1)$

Romeo Mestrovic

In this paper we prove that for any prime $p \geq 11$ holds $(p - 1 2 p - 1) \equiv 1 - 2 p k = 1 \sum p - 1 \frac{1}{k} + 4 p^{2} 1 \leq i < j \leq p - 1 \sum \frac{1}{ij} (mod p^{7}) .$ This is…

math.NT2011★ 6 cited

Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun

Romeo Mestrovic

For a positive integer $n$ let $H_{n} = \sum_{k = 1}^{n} 1/ k$ be the $n$ th harmonic number. In this note we prove that for any prime $p \geq 7$ , $$ \sum_{k=1}^{p-1}\frac{H_k^2}{k^2} \equiv4…

Two curious inequalities involving different means of two arguments

A primality criterion based on a Lucas' congruence

Variations of Lucas' Theorem Modulo Prime Powers

A search for primes p such that Euler number Ep−3​ is divisible by p

Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)

An Extension of a Congruence by Kohnen

Clarkson's type inequalities for positive lp​ sequences with p≥2

An Extension of a Congruence by Tauraso

Congruences for Wolstenholme primes

On the mod p2 determination of ∑k=1p−1​Hk​/(k⋅2k): another proof of a conjecture by Sun

An elementary proof of a congruence by Skula and Granville

On the mod p7 determination of (p−12p−1​)

Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun

A search for primes $p$ such that Euler number $E_{p - 3}$ is divisible by $p$

Clarkson's type inequalities for positive $l_{p}$ sequences with $p \geq 2$

On the mod $p^{2}$ determination of $\sum_{k = 1}^{p - 1} H_{k} / (k \cdot 2^{k})$ : another proof of a conjecture by Sun

On the mod $p^{7}$ determination of $(p - 1 2 p - 1)$