reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem
  n <= 1105 & n is composite & n divides 2|^n-2 & n divides 3|^n-3 implies
  n in {561,1105}
  proof
    assume n <= 1105 & n is composite & n divides 2|^n-2;
    then n in {341,561,645,1105} by Th49;
    then n = 341 or n = 561 or n = 645 or n = 1105 by ENUMSET1:def 2;
    hence thesis by Th50,Th56,TARSKI:def 2;
  end;
