How to write the direct proof of this

[noble crypt]

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[strong fiber]

This is my work so far:)

[willow phoenix]

this is bad style

what you mean is b = ac for some c, then taking d = 3a^2c^3 - ac^2+5c we have ad = ..

alternatively prove that a | b and a | c implies a | sb + tc for all integers s,t

by assumptions a | b, a | b^2 and a | b^3, the result follows

[strong fiber]

that makes a lot of sence, thank you very much @willow phoenix