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comment Natural density of primes congruent to m modulo N and to r modulo S
That should only be true if you expect that being relatively prime to $N$ and relatively prime to $S$ are essentially independent events. What condition on $N$ and $S$ do you need to make this a reasonable expectation?
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comment Rowspan of 0-1 Matrix
This seems to settle that the answer is no, thanks.
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comment Rowspan of 0-1 Matrix
Sure, good point. I wasn't considering the trivial case.
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comment Is $\frac{a+b}{c+d}<\frac{a}{c}+\frac{b}{d}?$, for $a,b,c,d>0$?
Or a = b = c = d = 1...
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accepted Bounding the Gamma Function
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answered Bounding the Gamma Function