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;
reserve f,g for complex-valued FinSequence;

theorem Th82:
  i is even implies i|^3 mod 8 = 0
  proof
    assume i is even;
    then consider j being Integer such that
A1: i = 2*j by ABIAN:11;
    thus i|^3 mod 8 = ((2|^3)*(j|^3)) mod 8 by A1,NEWTON:7
    .= ((2*2*2)*(j|^3)) mod 8 by POLYEQ_5:2
    .= 0 by BINARI_4:20;
  end;
