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Search: Posts Made By: Dr Sardonicus
Forum: Other Mathematical Topics 2019-12-21, 16:19
Replies: 5
Views: 4,827
Posted By Dr Sardonicus
I find the function F(z) \; = \;...

I find the function

F(z) \; = \; \prod_{i=1}^{\infty}(1 \; - \; z^{i})\text{, }|z|\;<\; 1

far more interesting than the decimal digits of its evaluation at a particular value of z. I note...
Forum: Other Mathematical Topics 2019-12-20, 15:13
Replies: 5
Views: 4,827
Posted By Dr Sardonicus
After a bit of quiet reflection on the well-known...

After a bit of quiet reflection on the well-known formula

\Phi_{n}(x)\;=\;\prod_{d\mid n}(x^{d} \; - \; 1)^{\mu(\frac{n}{d})}

I noticed that substituting x = 2 and doing a bit of rearranging...
Forum: Other Mathematical Topics 2019-12-19, 21:57
Replies: 5
Views: 4,827
Posted By Dr Sardonicus
I'm not sure what you mean to be asking. ...

I'm not sure what you mean to be asking. Obviously, the smallest positive integer congruent to 1 modulo any positive integer modulus m is 1.

If you want integers whose prime factors are...
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