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Mathematics
Linear and Abstract Algebra
Proving the Chinese Remainder Theorem for Reduced Residues Modulo mn
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[QUOTE="frowdow, post: 3105663, member: 304667"] I am teaching myself number theory using George Andrews book. i am stuck in the following problem: To prove that as x cycles thru' the reduced residue set modulo m & y cycles thru' reduced residue set modulo n, nx + my cycles thru' reduced residue set modulo mn. I am able to prove that: a) nx1 + my1 [STRIKE]=[/STRIKE] nx2 + my2 and b) nx + my is relatively prime to mn But how do i prove that nx + my cycles thru' every one of the reduced residue set modulo mn without first proving that [tex]\phi[/tex][tex]\left(xy\right)\neq[/tex][tex]\phi\left(x\right)\phi\left(y\right)[/tex] [/QUOTE]
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Linear and Abstract Algebra
Proving the Chinese Remainder Theorem for Reduced Residues Modulo mn
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