EUCLID'S DIVISION LEMMA
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In arithmetic, Euclidean division — or division with remainder — is the process of dividing one integer by another, in such a way that produces a quotient and a remainder smaller than the divisor. Its main property is that the quotient and the remainder exist and are unique, under some conditions.
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Euclid's Division lemma
It states that for any positive integer a and b there exists a uniques integer q and r such that
a = bq + r and
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