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Cyborg31
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Homework Statement
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
Homework Equations
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