Fractions, Floors, Arithmetic and Geometric Series!

\(a, b,\) and \(c\) are distinct positive integers less than 100.

How many ordered triples \((a, b, c)\) satisfy the following 2 conditions?

a) \(\left \lfloor \dfrac{a}{b} \right \rfloor, \left \lfloor \dfrac{b}{c} \right \rfloor, \left \lfloor \dfrac{c}{a} \right \rfloor\) are in an arithmetic progression in that order.

b) \(\left \lceil \dfrac{a}{b} \right \rceil, \left \lceil \dfrac{b}{c} \right \rceil, \left \lceil \dfrac{c}{a} \right \rceil\) are in a geometric progression in that order.

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