Recent content by peteryellow

Please somebody help me with this it is very urgent. I have that f(x) = x^5-5x+1 has S_5 as galois group over rationals. ANd M is the splitting field of f(x) over rationals. Then how can I show that : determine f(x) is irreducible over Q({-51}^{1/2})[x] or not? Determine if there is...

soory . t(n) = divisor function, i.e., number of positive divisors of n including n and 1. Then I want to show that t(n) < 2*(n)^{1/2}. I mean 2 times squareroot of n.

Let t(n) be the divisor function, i.e., the function gives the positive divisors in n including 1 and n. Then I want to show that $2n*(n)^{1/2}.$ I have tried different ideas but nothing is working can somebody please give some hints.

ok here it is the clear version of it. n=pqr is carmicahelnumber. if we have that r-1|pq-1 then I have shown that pq-1=d(r-1) where d is [2;p-1]. Moreover I have shown that q-1|d(r-1)-p+1. Now I want to show that if q-1|pr-1 is also fulfilled then q-1 is divisor in (d+p)(p-1). Do you...

$n=pqr$ is a Carmichael number. If $q-1|pr-1$ and $r-1|pq-1$ then show that q-1 is a divisor in $(d+p)(p-1).$

yes, but how.

I wish I was done but I am not how can I prove that P(x) \sim Li(x). P is different from /pi. Give any suggestion how can I prove this.

I have shown this but still I need to show that P(x) \sim Li(x).

We have that $P(x) = \sum_{k=1}^{\infty} \frac 1k \pi(x^{1/k})$ and $Li(x) = \int_2^n \frac {dt}{\log t}$ And the prime number theorem is: $$\pi(n) \sim \frac{n}{\log n }$$ I want to show that $$P(x) \sim Li(x)$$ is equivalent to prime number theorem. Can some body please...

My definition of a strongly nilpotent element is: Let a be in ring R the element a is strongly nilpotent if for every sequence a_0,a_1,...,a_i,... such that a_0 =a and a_{i+1} is in a_iRa_i, there exists an n with a_n =0. The question is in a theroem I am using that a is not strongly...

Simple ring M_n(F) where F is a field, but what is the definition of a simple domain?

Let V be a countable dimensional vectorspace over a field F . Let R denote End_F V . Prove that V is a simple R-module. If $ e1 , e2 , . . .$ is a basis of V , then we have a module homomorphism φ_j from R to V , sending f in R to f (e_j ). Find the ker(φ_j) . Find Jac(R). here I...

The functions K maps to f(K) and C maps to U(C) are given as: F(K) = aK and U(C) = -C^2 +b here a and b are positive constants. the initial and teriminal conditions with the triminal time T = 1/a are K(0) = K_0 and K_T = K(1/a) here K_0 and K_T are positive constants. Write Euler...

Can you find an example of a simple domain not being skew field?

But Morphism can you please tell me that what are prime and maximal ideals of the ring, and how can I FIND THEM. PLEASE HELP. THNAKS