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Im looking for answer, how to find inverse function for this function: $$f(x)=(51x+51)^{51} \bmod 107.$$

We can write it like this I suppose: $$ y=(51x+51)^{51} $$ $$y^{56}=51x+51 $$ $$y^{56}+56=51x $$ $$21*(y^{56}+56)=x$$ $$y=21*(x^{56}+56)$$, am I right?

Dawid
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jan 19 '24 at 18:40
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    Can you find the inverse of $51x+51$? What about $x^{51}$? – CyclotomicField Jan 19 '24 at 18:55
  • See the linked dupe for how to take the $51$'th root, using $,\frac{1}{51}\equiv 70\pmod{!106}.,$ The rest is easy. – Bill Dubuque Jan 19 '24 at 19:08
  • We can write it like this I suppose: $$ y=(51x+51)^{51} $$ $$y^{56}=51x+51 $$ $$y^{56}+56=51x $$ $$21(y^{56}+56)=x$$ $$y=21(x^{56}+56)$$, am I right? – Dawid Jan 19 '24 at 21:31

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