theorem
  for n be prime Nat, a,b be positive Nat holds
  n*a*b divides (a+t)|^n - (a|^n + b|^n) implies
    n*a*b divides (a+b)|^n - (a+t)|^n
  proof
    let n be prime Nat, a,b be positive Nat;
    assume
    A1: n*a*b divides (a+t)|^n - (a|^n + b|^n);
    n*a*b divides -((a+b)|^n - (a|^n + b|^n)) by INT_2:10,Th55; then
    n*a*b divides ((a|^n + b|^n) - (a+b)|^n) + ((a+t)|^n - (a|^n + b|^n))
      by A1,WSIERP_1:4; then
    n*a*b divides -((a+b)|^n - (a+t)|^n);
    hence thesis by INT_2:10;
  end;
