Recent content by nowimpsbball

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    Prove that x^100 = 1 for all x in U(1000)

    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...
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    Prove that x^100 = 1 for all x in U(1000)

    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
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    Prove that x^100 = 1 for all x in U(1000)

    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
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    Proving the Generating Function for 1/(z-1) Using Binomial Expansion

    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...
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    Roll 12 different dice. How many will have at least each 1,2,3,4,5,6 occurring?

    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...
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    Show that the probability of scroing exactly n points 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...
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    Given 2n objects, number of ways to select n objects

    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...
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    Placing 8 rooks onto a 8x8 chess board so no two share same row or column

    oh duh, because there are 8 different possibilities for each spot so 8!
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    Placing 8 rooks onto a 8x8 chess board so no two share same row or column

    So i should divide the first answer by 8, cool, thanks.
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    Placing 8 rooks onto a 8x8 chess board so no two share same row or column

    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...
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    Graduate A group G has exactly 8 elements or order 3

    g has 8 elements OF order 3, my bad
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    Graduate A group G has exactly 8 elements or order 3

    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...
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    Let A be A set of n Distinct Elements.

    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...