anonymous
  • anonymous
Using the least integer principle, define r to be least integer for which j - qk is positive. Prove that 0< r <=k
Mathematics
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anonymous
  • anonymous
Using the least integer principle, define r to be least integer for which j - qk is positive. Prove that 0< r <=k
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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zzr0ck3r
  • zzr0ck3r
? this shuold that q or j be an r?
anonymous
  • anonymous
Actually r= j - qk. This comes form Euclid's division lemma: j=qk + r
thomas5267
  • thomas5267
Is j and q positive or not?

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thomas5267
  • thomas5267
Proofwiki has a rigorous but rather hard to understand proof. Ask if you need help. https://proofwiki.org/wiki/Division_Theorem
anonymous
  • anonymous
I think I understood the informal proof. Just to make sure, when it says that: b∖(r−r0). −b

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