If c=ax+by and d|a but d does not divide c then prove that d does not divide b., Lecture7

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Proof involving "divides"

If c|a and c|b, then c|gcd(a, b)

If a|b and c|d, then ac|bd

Number Theory | The GCD as a linear combination.

a | b And c | d Does NOT Imply That (a+c) | (b+d)

(4.4.17) Proving a Division Property of Integers: If a Divides c and b Divides d, Then ab Divides cd

Proof: Divides Relation is Transitive (if a divides b and b divides c then a divides c)

If gcd(a,b)=1, d|ac, and d|bc, then d|c.