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?
Thanks
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$\begingroup$ because $a$ is the particular solution of $x^2\equiv 17 (\mod 128)$ $\endgroup$– VarazdaCommented Dec 23, 2017 at 18:06
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1 Answer
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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
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$\begingroup$ but why would $a$ be a solution in the first place? The author claims that $x=ay$ is the solution $\endgroup$ Commented Dec 23, 2017 at 18:22
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$\begingroup$ Oh, it's the author assumption - Thanks! $\endgroup$ Commented Dec 23, 2017 at 18:30