/sci/ - Science & Math

There is a theorem (I forget what it's called) that if K is the splitting field of f over Q, then if f factors as <span class="math">f(x) \equiv f_1(x) ... f_n(x) \mod p[/spoiler] then there exists an element in Gal(K/Q) thought of as a subgroup of S_d, where d = deg f, with cycle type (deg f_1, ..., deg f_n).

My question is simply: is the converse true? If I find an element with the proposed cycle type in Gal(K/Q), must f factor in that fashion modulo some prime p in Q? Also, are both statements true in the relative case (L/K, for arbitrary number fields)?

Even Neanderthals were much stronger than us. We're like, the weakest primates ever.

Hello /sci/
I saw a thread on /b/ and thought you guys would be more interested than they would, the objective is simple: solve the ciper
bonus if you figure out the algorithm

The Code is the following:

Wf gwj eys hrbsexg klj fwo awxg ey zrky flvi ylsix twr yw hegrui yfek wry.

Hints:

All I's are E's and all E's are I's.
All G's are G's and all V's are V's.

pic unrelated

>yfw he presses attempted murder charges on you

Sci can you help me with my math homework?

It's just one question that's stumping me.

"Bill has 4 apples that he wants to give to his children Jack and Jill. If bill wants to give both Jack and Jill the same number of apples how many apples will Bill give Jack?"

Physics 102
Chemistry 106
Bio 107

All next semester with some bullshit GER thrown in.

How fun is my second semester of freshmen year looking?