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

Let $$P_n(x) = 1 + \dfrac{1}{2}x - \dfrac{1}{8}x + \cdots + (-1)^n \dfrac{1.3.5 \cdots (2n - 3)}{2.4.6 \cdots 2n}x^n$$ Prove that if $\alpha = 8y + 1$ and $\alpha \geq 3$, then $P_{\alpha - 3}(8y)^2$ is a solution to $x^2 \equiv a \pmod{2^\alpha}$.

I'm really confused about that notation. Is $$P_{\alpha - 3}(8y)^2 = P_{\alpha - 3}(64y^2) \text{ or } P^2_{\alpha - 3}(8y) ?$$


share|cite|improve this question
You could always plug in some numbers and see which of the alternatives that seems to satisfy the statement that you're supposed to prove. (I'm too lazy to do that myself now.) :) – Hans Lundmark Apr 11 '11 at 8:24
This is certainly a good case for parentheses. As it is so easy to take the square inside in the first case, I'm with Gerry. – Ross Millikan Apr 11 '11 at 13:06
@Ross Millikan: Thank you. – Chan Apr 11 '11 at 17:36
up vote 5 down vote accepted

If I were to use that notation, I'd mean the second of your alternatives, not the first.

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.