Solve $x^{83}\equiv 7\pmod {139}$

Solve the congruence $x^{83}\equiv 7\pmod {139}$. 

Please explain your working at each stage as if you were teaching an undergraduate student who were learning this for the first time! I am really trying to learn how to solve these type of. Qs. I notice that both the mod and exponent are prime. I suspect that you might need to use a primitive root, and would appreciate extra insights/explanations of alternative approaches or methods. Ideally, I would like to learn the most efficient methods possible.


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Erdos Erdos
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