Note on the two congruences , , where is an odd prime and , , ,
Haridas Bagchi (1949)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Haridas Bagchi (1949)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Maohua Le (2006)
Czechoslovak Mathematical Journal
Similarity:
Let , , , be positive integers such that , , is even and is odd. In this paper we prove that if and either or is an odd prime power, then the equation has only the positive integer solution with .
Romeo Meštrović (2012)
Czechoslovak Mathematical Journal
Similarity:
In the paper we discuss the following type congruences: where is a prime, , , and are various positive integers with , and . Given positive integers and , denote by the set of all primes such that the above congruence holds for every pair of integers . Using Ljunggren’s and Jacobsthal’s type congruences, we establish several characterizations of sets and inclusion relations between them for various values and . In particular, we prove that for all , and...
Mariusz Ska/lba (2005)
Colloquium Mathematicae
Similarity:
A classical theorem of M. Fried [2] asserts that if non-zero integers have the property that for each prime number p there exists a quadratic residue mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].
Artūras Dubickas, Aivaras Novikas (2014)
Czechoslovak Mathematical Journal
Similarity:
Let , where and , and let be a sequence of integers given by the linear recurrence for . We show that there are a prime number and integers such that no element of the sequence defined by the above linear recurrence is divisible by . Furthermore, for any nonnegative integer there is a prime number and integers such that every element of the sequence defined as above modulo belongs to the set .
Florian Luca, Pantelimon Stănică (2003)
Colloquium Mathematicae
Similarity:
We show that if p ≠ 5 is a prime, then the numbers cover all the nonzero residue classes modulo p.
A. J. Irving (2015)
Acta Arithmetica
Similarity:
Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .