(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a, b < c, and d are positive integers, prove the following inferences.

1. a|b [itex] \wedge [/itex] c|d [itex]\rightarrow[/itex] ac|bd

2. a|b <=> ac|bc

2. Relevant equations

3. The attempt at a solution

1.

a|b = x, then b = ax

c|d = y, then d = cy

bd = axcy

thus ac|bd = ac|axcy, and ac|axcy = xy

therefore ac|bd = xy if a|b = x and c|d = y

2.

c|ac = a and c|bc = b

so c|(ac|bc) = a|b

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# Number Theory Division

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