Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

so far i can see that it has 3 solutions but im not sure where to find the others that the question hints at.

Show that the equation $y^2=4$ has at least four solutions in the ring $Z_5[x]/\langle x^2+1 \rangle $

share|cite|improve this question

Hint: The elements of the quotient can be written as $ax+b$, where $a$ and $b$ range from $-2$ to $2$. Note that $(ax+b)^2=a^2x^2 +(ab+ab)x +b^2$, which is $b^2-a^2 +(ab+ab)x$.

share|cite|improve this answer

Here are $4$ roots: $y_1 =2 ,y_2 =3 ,y_3 =\pm x.$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.