# Okay to post homework
# Ryan Badi, March 31, 2024, Homework 19

p := proc(n) local j, m:
  1 + sum(trunc(trunc((n / (1 + sum(trunc((1 + (j - 1)!) / j - trunc((j - 1)! / j)), j=2..m))))^(1 / n)), m=1..2^n):
end:

t := proc(n) local p:
  return 2 + n * trunc(1 / (1 + sum(trunc((n + 2) / p) - trunc((n + 1) / p), p=2..n+1))):
end:

myPi := proc(n):
  return trunc(sum(sin((Pi * GAMMA(k)) / (2 * k))^2, k=1..n))
end:

CommonKey := proc(P) local g, alicebob, bobalice, common, commonalice, commonbob:
  g := FindPrimi(P):
  alicebob := AliceToBob(P, g):
  bobalice := BobToAlice(P, g):
  commonalice := bobalice[2]&^(alicebob[1]) mod P:
  commonbob := alicebob[2]&^(bobalice[1]) mod P:
  common := g&^(alicebob[1]*bobalice[1]) mod P;
end:

for i from 1 to 5 do
 P := nextprime(rand(10^4..10^6)()):
 Verify(P):
od:

DL := proc(x, P, g) local a:
  if not x < 1 or x > P - 1 then:
    return FAIL:
  fi:

  for a from 1 to P - 1 do:
    if g^a = x then:
      return a:
    fi:
  od:

  return FAIL:
end: