I need to find the discrete logarithm of 20 modulo 71 where the generator of the group is 7. I need to break the group $|G|=2 \times 5 \times 7$ in subgroups $|G_1|=2, |G_2|=5, |G_3|=7$. I am new to this. Can someone please help me out?

Edit: Till now, I have reduced the above problem to the following system of equations (I don't know if I'm correct.):

\begin{align} 20^{35}&=(7^{35})^a\text{ in }G_1\\20^{14}&=(7^{14})^a\text{ in }G_2\\20^{10}&=(7^{10})^a\text{ in }G_3 \end{align}

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    $\begingroup$ Welcome to Cryptography. Since this is homework, look at this $\endgroup$
    – kelalaka
    Commented Apr 1, 2019 at 19:04
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    $\begingroup$ What have you tried? Does the name Pohlig–Hellman mean anything to you? $\endgroup$ Commented Apr 1, 2019 at 20:46
  • $\begingroup$ @SqueamishOssifrage No it doesn't. $\endgroup$ Commented Apr 2, 2019 at 9:27
  • $\begingroup$ @kelalaka Thank you. And it isn't homework but it was asked in the quiz. $\endgroup$ Commented Apr 2, 2019 at 9:27
  • $\begingroup$ You can post your solution. $\endgroup$
    – kelalaka
    Commented Apr 2, 2019 at 19:39


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