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).(adsbygoogle = window.adsbygoogle || []).push({});

Here's the conjecture.

Let [tex]X_n = r_1 \, r_2 \, r_3 \, ... \, r_n[/tex], be a product ofnrational fractions [tex](r_i)[/tex] , such that, for eachnin[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 asngoes toinfinityof [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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# A Conjecture : can anyone find a counter-example or otherwise disprove ?

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