Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by). Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b.
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Originally Posted by algebrapro18 Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by). Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b. d|a means there is an A so that a=dA. d|b means there is a B so that b=dB. Now ax+by = dAx + dBy = d(Ax+By) and so d|(ax+by).
Wow I can't believe I didn't see that...so easy. The reason I asked this is because my professor made it sound MUCH harder than this.
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