Recent content by audiowize

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    Graduate The Chinese Remainder Theorem for moduli that aren't relatively prime

    OK, I got that the gcd(n,m)|(a-b)-> x==a mod(n) and x==b mod(m) will have a solution, but showing that that solution is restricted to the modulus of m*n is giving me troubles...
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    Graduate The Chinese Remainder Theorem for moduli that aren't relatively prime

    Hello, I am looking into proving that the Chinese Remainder Theorem will work for two pairs of congruences IFF a congruent to b modulo(gcd(n,m)) for x congruent to a mod(n) and x congruent to b mod(m). I have gotten one direction, that given a solution to the congruences mod(m*n), then a...
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    Undergrad Proving Divisibility: How to Show b|a When b3|a2 - Helpful Tips"

    Hello, If we are given that b3|a2, how do we show that b|a? I started off looking at prime factorizations, but I could use a push in a more substantial direction.
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    Group Theory - specific non-abelian case

    Thanks for the help guys! I'm sure glad I don't have to take exams at midnight. A fresh set of eyes in the morning and your confirmation sure helped!
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    Group Theory - specific non-abelian case

    The permutation group S_3. I looked at this also... but the cubes of the individual elements seemed closed under the operation of composition, and the identity is present... Four of us have spent about 3 hours on this without much luck, any nudging is greatly appreciated!
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    Group Theory - specific non-abelian case

    Homework Statement Let G be an Abelian group and let H+{x^3 : x is an element of G} Find a non-Abelian group in which H is not a subgroup Homework Equations I wish it was that easy... The Attempt at a Solution I looked at the quaternion group, and some other matrix groups, but...