Recent content by regularngon

Thanks for the reply. I did a few computations and indeed it seems to only hold for when (p-1)/2 is also a prime. I still don't see how Little Fermat implies this though...

Homework Statement Find all primes p (as a congruence) such that 11^((p-1)/2) = 1 modp The Attempt at a Solution I'm new to congruences and I don't really know to approach this. Any help greatly appreciated!

Um how am I supposed to do long division if p is arbitrary?

First off it should be k roots in F, not K. Mystic I don't see how I find p that way, after all I have no way of figuring out the coefficients of the remainder. Buzz thanks for your help but that doesn't work.

I'm trying to prepare for finals, and these questions have me completely stumped. Homework Statement 1) For what primes p is x^2 + 1 a factor of x^3 + x^2 + 22x + 15 in F_p[x]? (F_p = finite field with p elements) 2) F a field. Let x^m - 1 have m distinct roots in F, suppose k divides m...

Yea it must be a typo on my teachers part. I'm going to guess he meant e^f(x).

for all n, and x > 0 though.

Homework Statement If 0 <= f(x) < infinity, then I need to show that e^x > (1 +f(x)/n)^n for x in (0, infinity) Homework Equations The Attempt at a Solution I'm pretty sure the answer lies in the comparison of the series representation for e^x and writing (1 +f(x)/n)^n out with...

Homework Statement Let R be a commutative ring and a,b in R. Show that the canonical image of ab in R/(f - f^2*g) is idempotent. Give an example where this idempotent is not 0 or 1. Homework Equations None. The Attempt at a Solution Well I've tried playing with the properties of...

No one has any suggestions? :cry:

Homework Statement Show that the function f : [0,1] × [0,1] → R given by f(x,y) = { 0 if x is irrational, or x is rational and y is irrational { 1/q if x is rational, y = p/q with gcd(p,q) = 1 Is integrable and compute the integral. Homework Equations The Attempt at a...

For introductory texts I'd recommend Munkres Topology for your topology part, and Marsden's Elementary Classical Analysis. It's easier than the texts you should have a look at after you do Marsden (Rudin's Principles of Analysis or Pugh's Real Mathematical Analysis), but not stupid like some...

Memorize all definitions and theorems if possible. That should be your first goal. Next, try to work through the proofs YOURSELF, only looking at a line from the text if you get stuck (not like 1 min stuck, like 30 min stuck!). Working through the text like that. Then last but not least try some...

My course is using Rudin, however I've heard that it's not the best text for learning measure theory and extremely difficult. What are some good supplements?

I am only supposed to assume the definition of the integral, which is why I'm stuck.