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
  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;
