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Why can't the product of two primes A and B be congruent to 0 modulo some other prime C? It's trivial that A * B can't be equal to C, but not as easy to show that it can't be 2 * C, say.


This was answered in the same comment tree before you posted the question: https://news.ycombinator.com/item?id=11953790


Yes, I know the proof. The point is that your original proof sketch didn't acknowledge the need for that lemma.




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