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Abhinav Anurag

CAT Preparation Community 10y ago

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..

1

Pv Aaditya 10y ago

Hi Abhinav,

172 mod 25 = 22

So, $$43 * 172^{142}$$ mod 25 = $$43 * 22^{142}$$ mod 25
$$22^{142} = 484^{71}$$
So, $$4*(43*172^{142} mod 25)$$ = $$4*(43*22^{142} mod 25)$$

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