Divisibility definition/proof

label Algebra
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Let a, b (= Z such that a not = 0. Use the definition of divisibility along with the Axioms of Integers 

If 15 | a and a | b, then 5 | (3a - 19b).

Mar 19th, 2015

By the definition, 15 | a means that a = 15*m for some integer m. Also, b = a*n = (15*m)*n = 15mn, where n is an integer.

Consequently,  3a - 19b = 45m - 19*15mn = 5*(9m - 57mn), and 5 | (3a - 19b).


Mar 19th, 2015

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Mar 19th, 2015
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Mar 19th, 2015
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