\ The\ value\ of\ 147^{23}\left(mod153\right)\ is
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= Rem [3*9^73 / 11]
= Rem [3*(-2)^73 / 11]
= Rem [3*(-2)^3*(-2)^70 / 11]
= Rem [3*(-8)*32^70 / 11]
= Rem [3*3*(-1)^70 / 11]
= Rem [9*(1) / 11]
= 9
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