Harry Gindi
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 Jun 25 awarded Teacher Aug 17 answered Math book for an eager learner with non-mathematical background Apr 15 comment Weak Dirichlet's theorem for powers of primes @KCd: The proof where I used Dirichlet's theorem proves it for all $a\in \mathbf{Z}$. You look $\sum_{d|n}\mu(n/d)a^d$ modulo $p^{\operatorname{ord}_p(n)}$. Then it splits into two cases, when $\operatorname{gcd}(p,a)=1$ and otherwise. You can use Dirichlet's theorem for the coprime case, and in the other case, you just follow your nose by looking at when the various Möbius terms vanish. Apr 14 comment Weak Dirichlet's theorem for powers of primes @KCd: I was just asking because I was proving the integrality (in general) of Gauss's formula whose value on $q=p^k$ is the the number of irreducible polynomials of degree $m$ in $F_q$. I ended up in a spot where I used Dirichlet's theorem, but I was reluctant to use such powerful technology, which is why I asked if perhaps there was a weaker form of Dirichlet's theorem that I could use instead. It appears that this is not the case. Apr 14 awarded Editor Apr 14 comment Weak Dirichlet's theorem for powers of primes Ah, thanks.  Apr 14 revised Weak Dirichlet's theorem for powers of primes added 5 characters in body Apr 14 asked Weak Dirichlet's theorem for powers of primes Mar 16 comment Counting the total-order extensions of |2| × |n| Thanks! I was thinking that perhaps the way to mess with it would be to take the transitive reflexive closure of the relation <, where a