Discrete Math Help with a Proof. Let a, b, and c be any integers. If a∣b, then a∣bc

Jonah Jacobson

Jonah Jacobson

Answered question

2022-09-07

Discrete Math Help with a Proof
I need help to prove the following: Let a, b, and c be any integers. If a∣b, then a∣bc

Answer & Explanation

rougertl

rougertl

Beginner2022-09-08Added 16 answers

Step 1
If a∣b then q Z : a q = b. So, a q c = b c. If you take Q = q c you see that Q Z : a Q = b c, therefore, a∣bc.
Now you can prove this one on your own for practicing:
If a∣b and c∣d then ac∣bd.
And this one:
Step 2
If a∣b and a∣c then a b x + c y for any x , y Z .
Just applying definitions should help you prove them straightforwardly.
Giancarlo Callahan

Giancarlo Callahan

Beginner2022-09-09Added 12 answers

Explanation:
If a∣b then b = a n for n Z. Then, b c = ( a n ) c and so a∣bc.

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