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 Th78:
  for k,l st k <> l & k+1 is odd prime & l+1 is odd prime
  holds 2*(k+1)*(l+1) divides a|^(k*l+1) - a
  proof
    let k,l such that
    A0: k <> l and
    A1: k+1 is odd prime & l+1 is odd prime;
    A2: k+1 <> l+1 by A0;
    k+1 divides a|^(k*l+1) - a & l+1 divides  a|^(k*l+1) - a by A1,Th73;  then
    A5: (k+1)*(l+1) divides a|^(k*l+1) - a by A1,A2,INT_2:30,PEPIN:4;
    A6: (k+1)*(l+1),2|^1 are_coprime by A1,NAT_5:3;
    2 divides a|^(1*(k*l)+1) - a by Th74; then
    2*((k+1)*(l+1)) divides a|^(k*l+1) - a by A5,A6,PEPIN:4;
    hence thesis;
  end;
