reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;

theorem Th34:
  k divides 5|^n implies k mod 4 = 1
  proof
    assume k divides 5|^n;
    then consider t being Element of NAT such that
A1: k = 5|^t and t <= n by PEPIN:34,59;
A2: 4*1+1 mod 4 = 1 mod 4 by NAT_D:21;
    5|^t mod 4 = (5 mod 4)|^t mod 4 by PEPIN:12;
    hence thesis by A1,A2,Lm3;
  end;
