Euclid's Division Lemma Consider the following folk puzzle*. A trader was moving along a road selling eggs. An idler who didn’t have much work to do, started to get the trader into a w
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Theorem 1.1(Euclid's Division Lemma) Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 \(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZ
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EXAMPLES 1 AND 2(Euclid's Division Lemma) Example 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576. Solution : Step 1 : Since 12576 > 4052, we apply the division lemm
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EXAMPLE 3 AND 4 (Euclid's Division Lemma) Example 3 : Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer. Solution : &nbs
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