Corpus ID: 119717397

Lucas' theorem: its generalizations, extensions and applications (1878--2014)

@inproceedings{Mevstrovic2014LucasTI,
  title={Lucas' theorem: its generalizations, extensions and applications (1878--2014)},
  author={Romeo Mevstrovi'c},
  year={2014}
}
  • Romeo Mevstrovi'c
  • Published 2014
  • Mathematics
  • In 1878É. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ( n m ) modulo a primep in terms of the binomial coefficients of the basep digits of n andm: If p is a prime,n = n0 + n1p + · · · + nsp andm = m0+m1p+· · ·+msp are thep-adic expansions of nonnegative integers n andm, then ( n 
    6 Citations
    Two Properties of Catalan-Larcombe-French Numbers
    Spatial equidistribution of combinatorial number schemes
    • 3
    • PDF
    Jacobi-Type Continued Fractions and Congruences for Binomial Coefficients
    Quantum Pascal's triangle and Sierpinski's carpet

    References

    SHOWING 1-10 OF 126 REFERENCES
    An extension of Lucas’ theorem
    • 41
    • Highly Influential
    • PDF
    Two p3 variations of Lucas' Theorem
    • 24
    A binomial sum related to Wolstenholme's theorem
    • 9
    • PDF
    Lucas' Theorem for Prime Powers
    • 39
    • PDF
    Catalan Numbers Modulo 2 k
    • 15
    • PDF
    Arithmetic properties of Apéry-like numbers
    • 6
    • PDF
    LUCAS-TYPE CONGRUENCES FOR CYCLOTOMIC -COEFFICIENTS
    • 12
    • PDF
    On divisibility of sums of Apery polynomials
    • 11
    • PDF
    Transcendence of Binomial and Lucas' Formal Power Series☆
    • 15