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 Th13:
  k is odd implies a|^n+1 divides a|^(n*k)+1
  proof
    assume k is odd;
    then consider b being Nat such that
A1: k = 2*b+1 by ABIAN:9;
    a|^n+1 divides a|^n|^(2*b+1) + 1|^(2*b+1) by NEWTON01:35;
    hence thesis by A1,NEWTON:9;
  end;
