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I have a problem in finding the solution of the equation given in the form of:$$153^{197}=x \mod 497$$ Can anyone hep me to solve this question?

user88595
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G.Senthil
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  • http://math.stackexchange.com/questions/81228/how-do-i-compute-ab-bmod-c-by-hand – user7530 Apr 16 '14 at 07:02
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    As $7\cdot71$

    $$153\equiv-1\pmod7\implies153^{197}\equiv(-1)^{197}\equiv-1$$

    and $$153\equiv11\pmod{71},197\equiv57\pmod{\phi(71)}; 153^{197}\equiv11^{57}\pmod{71}$$

     – lab bhattacharjee Apr 16 '14 at 07:04

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