reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem
  42 divides a|^(6*n+1) - a
  proof
    A0: 2,7 are_coprime & 3,7 are_coprime by INT_2:28,30,PEPIN:41,NAT_4:26;
    A1: 2 divides  a|^(6*n+1) - a by Th74;
    3 divides a|^(2*(3*n)+1) - a by Th75; then
    A2: 2*3 divides a|^(6*n+1) - a by INT_2:28,30,PEPIN:41,A1,PEPIN:4;
    7 divides a|^(6*n+1) - a by Th77; then
    7*(2*3) divides a|^(6*n+1) - a by A0,EULER_1:14,A2,PEPIN:4;
    hence thesis;
  end;
