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uart

Science Advisor

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Hi, I have a conjecture and I am not sure whether it is true. I can't construct a counter example but perhaps someone more mathemetically resourceful than myself can do so (or perhaps even offer a direct proof or disproof).

Let [tex]X_n = r_1 \, r_2 \, r_3 \, ... \, r_n[/tex], be a product of

Conjecture : If the limit as

If you cant find a counter-example (or direct proof or disproof) then what does your mathematical "intuition" think about it, do you think it's probably true or probably false.

Thankyou. :)

**Here's the conjecture.**Let [tex]X_n = r_1 \, r_2 \, r_3 \, ... \, r_n[/tex], be a product of

**n**rational fractions [tex](r_i)[/tex] , such that, for each**n**in**[1,2,3 …]**the numerator of [tex]X_n[/tex] has at least one prime factor (uncancelled of course) greater than n.Conjecture : If the limit as

**n**goes to**infinity**of [tex]X_n[/tex] is finite then it (the limit) is irrational.If you cant find a counter-example (or direct proof or disproof) then what does your mathematical "intuition" think about it, do you think it's probably true or probably false.

Thankyou. :)

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