A generalization of a necessary and sufficient condition for primality due to Vantieghem.
Kilford, L.J.P. (2004)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “-analogue of a binomial coefficient congruence.”
A generalization of a necessary and sufficient condition for primality due to Vantieghem.
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Visible Points on Curves over Finite Fields
Igor E. Shparlinski, José Felipe Voloch (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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For a prime p and an absolutely irreducible modulo p polynomial f(U,V) ∈ ℤ[U,V] we obtain an asymptotic formula for the number of solutions to the congruence f(x,y) ≡ a (mod p) in positive integers x ≤ X, y ≤ Y, with the additional condition gcd(x,y) = 1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average over a for a fixed prime p, and also on average over p for a fixed integer a.
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Noe, Tony D. (2006)
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On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (completion of Mordell's proof)
A. Schinzel (2015)
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Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.
Equality in Pollard's theorem on set addition of congruence classes
E. Nazarewicz, M. O'Brien, M. O'Neill, C. Staples (2007)
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Leudesdorf's theorem and Bernoulli numbers
I. Sh. Slavutsky (1999)
Archivum Mathematicum
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For , , it is proved the relations between the sums and Bernoulli numbers. The result supplements the known theorems of C. Leudesdorf, N. Rama Rao and others. As the application it is obtained some connections between the sums and Agoh’s functions, Wilson quotients, the indices irregularity of Bernoulli numbers.