theorem
  for n be prime Nat, a,b be positive Nat holds
    n*a*b divides (a+b)|^(k*n) - (a|^n + b|^n)|^k
proof
  let n be prime Nat, a,b be positive Nat;
  (a+b)|^n - (a|^n + b|^n) divides ((a+b)|^n)|^k - (a|^n + b|^n)|^k
    by NEWTON01:33; then
  A1: (a+b)|^n - (a|^n + b|^n) divides (a+b)|^(k*n) - (a|^n + b|^n)|^k
    by NEWTON:9;
  n*a*b divides (a+b)|^n - (a|^n + b|^n) by Th55;
  hence thesis by A1,INT_2:9;
end;
