theorem
  for n be prime Nat, a,b,c be positive Nat holds
  n*a*b divides c-b implies n*a*b divides (a|^n + b|^n) - (a+c)|^n
  proof
    let n be prime Nat, a,b,c be positive Nat;
    assume n*a*b divides c-b; then
    n*a*b divides -(b-c); then
    A1:  n*a*b divides b-c by INT_2:10;
    (a+b) - (a+c)  divides (a+b)|^n - (a+c)|^n by NEWTON01:33; then
    A3: n*a*b divides (a+b)|^n - (a+c)|^n by A1,INT_2:9;
    n*a*b divides -((a+b)|^n - (a|^n + b|^n)) by INT_2:10,Th55; then
    n*a*b divides (a+b)|^n - (a+c)|^n + -((a+b)|^n - (a|^n + b|^n))
      by A3,WSIERP_1:4;
    hence thesis;
  end;
