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;
