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 Jan 6 answered Bounding sums of residue classes Dec 8 revised If $\sum_{r=1}^{n} t_r$ = ${ n ( n + 1 ) ( n + 2 ) ( n + 3 ) } \over {8}$ , then what does $\sum_{r=1}^{n} {1\over {t_r} }$ equal to? added 1 character in body Dec 8 answered If $\sum_{r=1}^{n} t_r$ = ${ n ( n + 1 ) ( n + 2 ) ( n + 3 ) } \over {8}$ , then what does $\sum_{r=1}^{n} {1\over {t_r} }$ equal to? Dec 5 revised A Dirichlet Convolution involving $\mu(n)$ and $\log n$ added 1 character in body Nov 22 awarded Yearling Nov 20 awarded Nice Answer Nov 11 awarded Popular Question Nov 3 awarded Popular Question Oct 30 comment Number of solutions to $x_1x_2+x_3x_4 = 1$ (mod $n$) Oct 24 comment Algorithm for finding all roots of linear Diophantine equation with finite solution space I'd first make the substitution $b_n-10=a_n$ so that your problem reduces to finding solutions to: $$17b_1+16b_2+\dots+2b_{16}+b_{17}=1530-c$$ $$b_n\in\{0,1,2,3,\cdots 18,19,20\}$$ Oct 19 comment Prove $∑^{(p−1)/2}_{k=1} \left \lfloor{\frac{2ak}{p}}\right \rfloor \equiv ∑^{(p−1)/2}_{k=1} \left \lfloor{\frac{ak}{p}}\right \rfloor ($mod $2)$ $$\lfloor{x}\rfloor=\sum_{n\leq x}1=\sum_{r=0}^{m-1}\sum_{{an+r\leq x}}1=\sum_{r=0}^{m-1}\sum_{{n\leq \frac{x-r}{a}}}1=\sum_{r=0}^{m-1}\lfloor{\frac{x-r}{m}}\rfloor$$ Oct 19 revised Estimates of the sum involving both the Mobius function and Mertens function. edited body Sep 6 awarded Nice Question Aug 23 awarded Pundit Jul 2 awarded Revival Jun 25 reviewed Approve $n! \le n^n$, $\forall$ $n \ge 1$. May 22 revised Ways of disproving proofs of the Collatz Conjecture? added 15 characters in body Apr 23 revised Möbius sums and Eulers totient function added 3 characters in body Mar 29 revised Summations involving $\sum_k{x^{e^k}}$ added 2 characters in body Mar 11 answered Summations involving $\sum_k{x^{e^k}}$