In the concept theory of factors and cyclicity,there is description as: 172^143 mod 100 = 172*172^142mod 100 = 4*(43*172^142mod25) = 4*(43*22^142mod25) = 4*(43*484^71mod 25)...So how the value of 43*172^142mod 25 has been simplified to 43*22^142mod25 and futher..Can u please elaborate this step..