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I'm stuck with another induction proof.

Question: Suppose a, b1, b2,...,bn are integers with a|b1 (means a divides b), a|b2, ..., a|bn. Prove by induction on n that a|b1x1 + b2x2 + ... + bnxn for all integers x1, x2,..., xn.

This is what i've, please let me know if it's correct. The question basically have connection of Proposition division alogrithm.

Base case:

Show that result is true for n = 1;

Since it's already given that when n = 1 then a|b1

therefore we can write b1 = aq for some inetger q. So b1x1 = aq(x1) = a(qx1) where q and x1 are integers. Hence a|bx1. Therefore, result holds for n = 1

Induction hypothesis: Assume reuslt holds for n = k.

I'm not too sure what to do next? Please someone help me with this, thanks in advance!

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# Homework Help: Another induction proof

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