Euclid's division lemma: for positive integers a and b there exist uni…

Question

Euclid's division lemma: for positive integers a and b there exist unique integers q and r with a = bq + r and:

Accepted Answer

A. 0 <= r < b

1. The remainder is smaller than the divisor.
2. It can be zero.
3. So 0 is at most r, and r is less than b.
_Source: syllabus Mathematics, Chapter 1, Real Numbers._

Answer

0 < r <= b

Answer

b <= r < a

Answer

r >= a > b

Euclid's division lemma: for positive integers a and b there exist unique integers q and r with a = bq + r and:

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