I'm trying to understand this answer.

I don't understand why $(ay)^2\equiv 17\pmod{128}$ iff $y^2\equiv 1\pmod{128}$

Could you please explain it to me?


  • $\begingroup$ because $a$ is the particular solution of $x^2\equiv 17 (\mod 128)$ $\endgroup$ Dec 23, 2017 at 18:06

1 Answer 1


You have, $$a^2\equiv 17 \pmod{128}$$ hence if, $$y^2\equiv 1 \pmod{128} $$ then, $$ a^2y^2\equiv 17 \pmod{128}$$ i hope it is clear this way

  • $\begingroup$ but why would $a$ be a solution in the first place? The author claims that $x=ay$ is the solution $\endgroup$ Dec 23, 2017 at 18:22
  • $\begingroup$ Oh, it's the author assumption - Thanks! $\endgroup$ Dec 23, 2017 at 18:30

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