History [of Pascal's triangle mod *k*]

Pascal's triangle probably dates from antiquity; it was known in China in the 1200s, and was discussed in some detail by Blaise Pascal in 1654, particularly in connection with probability theory. The digit-based approach to finding binomial coefficients modulo k has been invented independently many times since the mid-1800s, notably by Edouard Lucas in 1877 and James Glaisher in 1899. The fact that the odd binomial coefficients form a nested geometrical pattern had apparently not been widely noticed before I emphasized it in 1982.