Number Theory: Section 2-1: Proof by Contradiction.

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In this video we will continue to solve problems from Number Theory by George E. Andrews. The problem is number 1 from Section 2-1(Euler Division Lemma) and illustrates a proof by contradiction.
  1. Zero_to_Hero
  2. education
  3. math
  4. number theory
  5. induction
  6. mathematical induction
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I'm hoping you are still on YT for this question. For 2-1 problem 2, I'm confused about proving 0<r<=k where r is the least integer such that j-qk is positive. I'm thinking the author is loose about integers vs natural numbers? This is confusing since sometimes he states an integer greater than zero. Anyways...

Suppose we have pair j=1, k=2. the only solution is if q<=0. But r is supposed to be the least value and is supposedly greater than 0. Am I being dumb? Lol

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