an interesting algebra problem

Probability 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 { $a_{1}$ , $a_{2}$ ................ , $a_{2006}$ } ?

The answer is 46.

1 solution

U Z
Sep 24, 2014

its very simple I will give you a hint that With 45 different positive integers we can only get 45 X 44 + 1 = 1981 fractions.
so there are more than 45 numbers in the set

an interesting algebra problem

The answer is 46.

1 solution

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