Douglas S. Stones
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 Oct11 comment Perfect numbers less than 10 000 I'm not sure in Maple, but in GAP they can be found using Filtered([1..9999],i->Sum(DivisorsInt(i))=2*i); which returns [ 6, 28, 496, 8128 ]. It's just brute force computation; nothing intelligent. Oct10 comment New hourly rate after a pay raise Does one really get 3 dollars for answering this question? I find that hard to believe. But, if it were true, by crowdsourcing, we don't even need to know any maths to make money. We can just copy/paste the questions here, and copy/paste the answers back for profit. Nice! Sep24 comment Re-write $1 \cdot x$ to $x$. A large chunk of Adriano's proof (and the Prover9 proof) amounts to showing that $(x^{-1})^{-1}=x$. If we can assume this: $$1x=(xx^{-1})x=x(x^{-1}x)=x(x^{-1}(x^{-1})^{-1})=x1=x.$$ Sep15 comment Show Continuity Using Epsilon Delta Definiton What happens if you attempt to do what it asks? Sep9 comment Finding the last two digits of a number by binomial theorem Does, "compute the number" count as any other way? The number is 108347059433883722041830251. Sep5 comment Solving a system of equations using modular arithmetic modulo 5 Print(Concatenation([":",")"]),"\n"); Sep2 comment Find the sum of all 4-digit numbers formed by using digits 0, 2, 3, 5 and 8? I know how you feel. But it is useful to know how to solve problems computationally too, even if it is just to check human-written solutions. (By the way, what language is this?) Aug31 comment In how many ways can three numbers be selected from the numbers $1,2,\dots,300$ such that their sum is divisible by $3$? Aside from the above, I found yours the best answer. Right to the point! Aug31 comment In how many ways can three numbers be selected from the numbers $1,2,\dots,300$ such that their sum is divisible by $3$? I'd say the answer to that question is yes (but I don't know what it is). Aug31 comment In how many ways can three numbers be selected from the numbers $1,2,\dots,300$ such that their sum is divisible by $3$? In the $(0,1,2)$ case, we can choose $100^3$ triples. Aug30 comment For what $n$ can $\pm 1\pm 2\pm 3 … \pm (n-1) \pm n = n+1$? That's an assertion. Could you add a proof of this assertion into this answer? Aug30 comment Find order of $xy$ provided $x^2=e, y^3=e$ and $yxy=xy^2x$ It's somewhat implicit that saying e.g. "$x^2=e$" implies $x$ has order $2$, otherwise we'd instead say "$x=e$" (or not even introduce $x$). Perhaps I'm a bit too pedantic (but this kind of detail matters e.g. for automated theorem proving). Anyway, the answer is fine so I better +1 it. Aug30 comment Find order of $xy$ provided $x^2=e, y^3=e$ and $yxy=xy^2x$ Hmm... it could be that $x=e=y$ too (in which case $xy=e$ has order $1$). The question doesn't say e.g. "the order of $x$ is $2$". [It must be a divisor of 3, though. So it's either $3$ or $1$.] Aug29 comment Problem on directed graph involving $\gcd$ The question for strongly connected digraphs is now here. Aug29 comment Problem on directed graph involving $\gcd$ It looks like a counterexample to me. I wonder if this is a homework question; the lecturer might have a surprise when the assignments are returned. (I suppose the theorem would be true if there were no "incoherent" cycles.) Aug29 comment Problem on directed graph involving $\gcd$ What is the value of $p$ if $G$ has no cycles? Aug29 comment Calculate the Determinant? I neatened this answer up a bit, and also corrected the arithmetic. Aug28 comment Have you seen this formula for factorial? This works then: $n!=\prod_{p^a \leq n} p^{\lfloor n/p^a \rfloor}$ where the sum is over all primes $p$ and $a \geq 1$ such that $p^a \leq n$. Aug28 comment Have you seen this formula for factorial? I'm wondering if it can be fixed by using something like "prime power p" or something similar. It's still not right, but a correction term perhaps could be introduced. Aug28 comment Have you seen this formula for factorial? Wrong, as in it's not right. E.g., $4!=24$ and $\prod_{p \leq 4} p^{\lfloor 4/p \rfloor}=2^2 \times 3=12$.