Aryabhata
Reputation
56,803
397/400 score
 9h comment $g^q-q$ and $g^q-gq$ are primitive roots modulo $q^2$ Using $g$ and $q$ is confusing! Apr26 comment Reduction from Hamiltonian cycle to Hamiltonian path @graphtheory92: Seems valid to me. What are your concerns? Apr17 comment Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$ Please use more informative titles. Apr17 comment How can I find if $\sum_{n=1}^\infty {n! \over 10^n}$ converges or diverges? Please use more informative titles. The previous title you had, was on par with "Help!". Apr17 comment Simplifying Sum @Guest: Using binomial theorem. It is a standard technique. You don't need to know RHS for it. Apr16 comment Simplifying Sum Without the algebra precalculus tag, the left side is $$\int_{0}^{1} (1-x)^n x^m \text{d}x$$ which is a Beta integral... Mar29 comment Diophantine system of two equations with four variables +1: More accessible to a 9th grader, than complex numbers I suppose. Mar28 comment Counting the number of integers $i$ such that $\sigma(i)$ is even. Is this an algorithm problem? Assuming it is, retagging as elementary-number-theory. Mar26 comment Calculation of limit without stirling approximation A previous answer of mine proves this in a completely elementary fashion: math.stackexchange.com/a/131084/1102. Falls right out of Proposition E. Mar26 comment Can the sum of reciprocals of a set without density converge? Convergence implies density is zero. See: math.stackexchange.com/questions/5932/… Mar19 comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$ +1: Nice....... Mar19 comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$ This is not pedantry. I don't think this is as trivial as you seem to be implying. Unless you have a proof, you are just handwaving. Anyway, you are free not to elaborate, and I am free to leave the downvote intact. Mar19 comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$ Please take at least a day or two before accepting an answer. In this case, the accepted answer is incomplete. Mar19 comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$ The heuristic is only a first step. Making it rigorous is the hard part. -1 till there is a proof. Sorry. Mar18 comment Quotient of a regular language @AstroNauft: You don't need to determine anything. It is a non-constructive proof. $L$ could be any language. Mar18 comment The limit : $\lim _{x \to \infty } \sqrt{x^2 +x} - \sqrt{x^2 +1}$ Mar17 comment How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$? @ADG: It is my name, I will spell it as I want! :-). Just kidding :-). Apparently, it is actually Aryabhata and not Aryabhatta. In fact I had it as Aryabhatta till ShreevatsaR corrected me. Mar8 comment Inequality between real numbers $a^ab^bc^c<(abc)^{\frac{a+b+c}{3}}$ If I haven't made any mistake that is... This looks too simple! Feb10 comment Comparing $\pi^{e}$ and $e^{\pi}$ @NikolajK: Thank you for the suggestion! Done. Feb1 comment Irrational numbers in reality @AsafKaragila: Thanks! Did not know the 60 day thing. The flag was declined with a comment that this is not about physics (which I disagree with) and it is too late to migrate (they didn't mention the 60 day thing).