3.9, due october 18th

i was a little confused about how a negative number could have a square root if the positive of it didn’t have one. i was pretty sure that negative numbers don’t have real square roots. but then i read through an example and i realized that it was the negative number (mod n) so it makes sense how it would have a root. again, it’s hard for me to just read through examples and understand them. these seem pretty simple, but i probably won’t really understand them until i do some examples by hand.

i think it’s so interesting what we can do with math.it’s also interesting to me how helpful modular arithmetic can be. we can find all solutions of x^2 congruent to b(mod n). it’s also interesting that if there isn’t a root for a number, then its negative will have a root. i love math!