Well that is the problem how it is stated...but the idiot I am keeps forgetting to mention all the details of U(n)...it is the group of units modulo n (that is the set of integers less than n and relatively prime to n under multiplication modulo n). But what you say is what I want.
I for...
Huh? Well U(1000) is all numbers less than a 1000 and relatively prime to 1000, that changes things, at least with your counter example...forgot to mention that
Homework Statement
Prove that x^100 = 1 for all x in U(1000)
Homework Equations
The Attempt at a Solution
U(1000) is all numbers relatively prime to 1000. And that is as far as I have gotten.
Thanks
Homework Statement
Prove that the generating function 1/(1-z) = (1+z)(1+z^2)(1+z^4)(1+z^8)...
which is also to 1+z+z^2+z^3+z^4+... when you multiply out the binomials. Homework Equations
(1/(1-z))^k = {\Sigma[from i=0 to infinity] C(i+k-1, k-1)z^i}The Attempt at a Solution
I've been playing...
Homework Statement
12 different dice are rolled. How many outcomes will have at least one of each number 1,2,3,4,5,6 occurring?
The Attempt at a Solution
I don't even know where to go because I really don't know what the question is asking. Does it mean how many rolls (where each roll is...
Homework Statement
A player tosses a coin repeatedly. Heads is one point, tails is two points. A player tosses until his score equals or exceeds n. Show that the probability of scoring exactly n points is (2+(-1/2)^n)/3
Homework Equations
The Attempt at a Solution
My guess...
Homework Statement
Given N identical objects and N additional objects that are different from these and from each other, find the number of ways to select n objects out of these 2N objects.
Homework Equations
Either P(n,k) or C(n,k) or n^k or maybe even (n+k+1)/k
The Attempt at a...
Homework Statement
In how many ways can eight identical rooks be placed on an ordinary 8x8 chessboard so that no two are in the same row or column? In how many ways, if each rook has a different color?
Homework Equations
I looked at the equation n choose k (nck), but I don't know if...
A group G has exactly 8 elements of order 3 (Unanswered as of 1/31)
How many subgroups of order 3 does G have?
So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so...
Let A be a set of n distinct elements. There is a one to one correspondence between binary relations on the set A and subsets R<= A x A
a. Computer the number of binary realtions on A
b. A binary relation R is said to be symmetric if for every (a,b) in R, (b,a) is also in R. Compute the...