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Let $S$ be the set of all rational numbers expressible in the form $$\frac{(a_1^2+a_1-1)(a_2^2+a_2-1)\ldots (a_n^2+a_n-1)}{(b_1^2+b_1-1)(b_2^2+b_2-1)\ldots (b_n^2+b_n-1)}$$ for some positive integers $n, a_1, a_2 ,\ldots, a_n, b_1, b_2, \ldots, b_n$. Prove that there is an infinite number of primes in $S$

This problem is from:http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3036693&sid=b7461a1fd2a06894c98e7c3ab04ac59e#p3036693

and my teacher tell me this link post solution is not true,so How prove it? Thank you

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Why do you think the given proof is not valid? –  anorton Feb 4 at 16:57

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