let a,b, be elements Z (integers) with a divides b proove a*n divides b*n for every positive integer n.?

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let a,b, be elements Z (integers) with a divides b proove an divides bn for every positive integer n.?

2006-09-09 05:53:36 · 2 answers · asked by thamal3 1 in Science & Mathematics ➔ Mathematics

2 answers

Congratulations Sir! You are a genius.

2006-09-09 05:57:12 · answer #1 · answered by ash_m_79 6 · 0⤊ 0⤋

let a,b e Z

a|b <=> there exists k e Z, b = k * a

suppose that's true ...

then b * n = (k * a) * n = (a * n) * k

so, then exists k e Z, (a*n) * k = b * n,

therefore (a*n) | (b*n)

2006-09-09 12:59:23 · answer #2 · answered by cybrdng 2 · 0⤊ 0⤋