Abstract Alg. Proof w/ Mod Congruence and Relative Primes

  • Thread starter Colleen G
  • Start date
  • #1
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Homework Statement


If ≡(mod), ≡(mod),and gcd(,)=1,provethat ≡ (mod ).


Homework Equations


If ≡(mod)→n|ab-cd
≡(mod)→n|b-d
gcd(,)=1→ relatively prime. So bx+ny=1

Need to show n|a-c→a-c=nw

The Attempt at a Solution


If n|ab-cd, then nk=ab-cd
If n|b-d, then nl=b-d
If n|ab-cd AND n|b-d, then n|p(ab-cd)+q(b-d). So pab-pcd+qb-qd.
pad-pcd+qb-qd
=pab+qb-pcd-qd
=b(pa+q) +d(-pc-q)

I'm stuck! Don't know if this is going anywhere.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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1,513

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