# an interesting algebra problem

Discrete Mathematics Level 3

Suppose that positive integers $$a_{1}$$ , $$a_{2}$$, .., $$a_{2 006}$$ (some of them may be equal) satisfy the condition: that any two of -

$$a_{1}/a_{2} , a_{2}/a_{3} , ........................,a_{2005}/{a_{2006}}$$

are unequal. At least how many different numbers are there in { $$a_{1}$$ , $$a_{2}$$ ................ , $$a_{2006}$$ } ?

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