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Eculid division lemme |
| Answer» Euclid’s Division Lemma:A lemma is a proven statement used for proving another statement.Theorem 1: “Given positive integers a & b, there exist unique integers q & r satisfying a = b*q + r, 0 ≤ r < b”.E.g. let’s assume that you have 34 apples & you have box that can accommodate 10 apples, then you have put these Apple in 3 boxes & you will have 4 apples remaining. Also note that the remaining apples are less than box size that is 10.34 Apples = 10 Apples * 3 Box + 4 Apples\xa0If you compare this with Euclid’s Division Lemma\xa0a = b*q + r, 0 ≤ r < b,\xa0Then a = 34, b=10, q=3 & r =4, 0 ≤ 4 <10 | |