Find all solutions in Z16 to the equation $\displaystyle x^2 =9$.

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- Nov 24th 2009, 03:54 PM450081592Find all solutions in Z16
Find all solutions in Z16 to the equation $\displaystyle x^2 =9$.

- Nov 24th 2009, 06:46 PMHallsofIvy
- Nov 24th 2009, 09:05 PM450081592
- Nov 25th 2009, 04:08 AMHallsofIvy
A matrix? Just do the arithmetic!

$\displaystyle 0^2= ?$

$\displaystyle 1^2= ?$

$\displaystyle 2^2= ?$

$\displaystyle 3^2= ?$

$\displaystyle 4^2= ?$

$\displaystyle 5^2= ?$

$\displaystyle 6^2= ?$

$\displaystyle 7^2= ?$

$\displaystyle 8^2= ?$

$\displaystyle 9^2= ?$

$\displaystyle 10^2= ?$

$\displaystyle 11^2= ?$

$\displaystyle 12^2= ?$

$\displaystyle 13^2= ?$

$\displaystyle 14^2= ?$

$\displaystyle 15^2= ?$

All of those are "modulo 16" of course. For example $\displaystyle 10^2= 100= 96+ 4= 6(16)+ 4$ so $\displaystyle 10^2= 4 (mod 16)$. - Nov 25th 2009, 08:53 AM450081592
- Nov 25th 2009, 09:07 AMtonio
- Nov 25th 2009, 09:10 AM450081592