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Post Closed as "off topic" by Felipe Voloch, Chris Godsil, Charles Matthews, Franz Lemmermeyer, Chandan Singh Dalawat
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Jim White
Jim White
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My question relates to square roots of unity modulo a squareN, ie $r^2 = 1 \mod N^2$$r^2 = 1 \mod N$.

For anyI have an efficient algorithm for obtaining these for arbitrary $f|N$, I'd like$N$. But for a given $N$ what I really want is to obtain the square roots of unity modfor all $\frac {N^2}{f^2}$$N_f = \frac {N^2}{f^2}$ for all $f|N$.

My question is simply this - can these all be deduced from the square roots of unity mod $N$? Or do I need multiple invocations of my root finder?

My question relates to square roots of unity modulo a square, ie $r^2 = 1 \mod N^2$.

For any $f|N$, I'd like to obtain the square roots of unity mod $\frac {N^2}{f^2}$.

My question is simply this - can these all be deduced from the square roots of unity mod $N$?

My question relates to square roots of unity modulo N, ie $r^2 = 1 \mod N$.

I have an efficient algorithm for obtaining these for arbitrary $N$. But for a given $N$ what I really want is to obtain the roots for all $N_f = \frac {N^2}{f^2}$ for all $f|N$.

My question is simply this - can these all be deduced from the square roots of unity mod $N$? Or do I need multiple invocations of my root finder?

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Jim White
Jim White
  • 225
  • 1
  • 7

Square Roots of Unity modulo N^2

My question relates to square roots of unity modulo a square, ie $r^2 = 1 \mod N^2$.

For any $f|N$, I'd like to obtain the square roots of unity mod $\frac {N^2}{f^2}$.

My question is simply this - can these all be deduced from the square roots of unity mod $N$?