reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th49:
  p is prime & i,p are_coprime implies order(i,p) divides p-'1
proof
  assume that
A1: p is prime and
A2: i,p are_coprime;
  (i |^ (p -'1)) mod p = 1 & p > 1 by A1,A2,Th37,INT_2:def 4;
  hence thesis by A2,Th47;
end;
