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anonymous

  • one year ago

Using the least integer principle, define r to be least integer for which j - qk is positive. Prove that 0< r <=k

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  1. zzr0ck3r
    • one year ago
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    ? this shuold that q or j be an r?

  2. anonymous
    • one year ago
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    Actually r= j - qk. This comes form Euclid's division lemma: j=qk + r

  3. thomas5267
    • one year ago
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    Is j and q positive or not?

  4. thomas5267
    • one year ago
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    Proofwiki has a rigorous but rather hard to understand proof. Ask if you need help. https://proofwiki.org/wiki/Division_Theorem

  5. anonymous
    • one year ago
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    I think I understood the informal proof. Just to make sure, when it says that: b∖(r−r0). −b<r−r0<b. Hence, r−r0=0 r-r0 must be 0 because there is no other way it is divisible by b. Am I right?

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