galois.ipynb

Kernel: SageMath (stable)

n=75
k=17
p=11

d=[n.digits(p),k.digits(base=p,padto=n.ndigits(base=p))]
d

[[9, 6], [6, 1]]

[[binomial(d[0][i],d[1][i]).mod(p) for i in range(len(n.digits(p)))],binomial(n,k).mod(p)]

[[7, 6], 9]

n.ndigits?

3.digits(base=5,padto=51.ndigits(base=5))

[3, 0, 0]

(12*22).mod(23)

11

8*23

184

pt=[binomial(513,k).mod(23) for k in [0..513]]

pos=filter(lambda k:k>0,pt)

len(pos)

184