On congruences for binomial coefficients
Copyright policy )On congruences for binomial coefficients
For primes \(p=1+4f=a^ 2+b^ 2\), \(a\equiv 1 (mod 4)\), Gauss proved that \(\left( \begin{matrix} 2f\\ f\end{matrix} \right)\equiv 2a (mod p)\). For primes \(p=1+kf\) (k\(\geq 3)\), many congruences modulo p, for the binomial coefficients \(\left( \begin{matrix} rf\\ sf\end{matrix} \right)\) \((0
- Chinese University of Hong Kong China (People's Republic of)
Algebra and Number Theory, Gross-Koblitz formula, Fibonacci and Lucas numbers and polynomials and generalizations, binomial coefficients, p-adic gamma function, Congruences; primitive roots; residue systems, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Factorials, binomial coefficients, combinatorial functions, congruences modulo prime squares
Algebra and Number Theory, Gross-Koblitz formula, Fibonacci and Lucas numbers and polynomials and generalizations, binomial coefficients, p-adic gamma function, Congruences; primitive roots; residue systems, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Factorials, binomial coefficients, combinatorial functions, congruences modulo prime squares
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