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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).
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 can't 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 can't 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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