Gamamal
Reputation
28,065
359/400 score
 May18 comment Prove or disprove: If $a^2 \mid bc$, then $a \mid b$ or $a \mid c$ Sure, happy to help. May18 comment Endomorphic Function Definition No, I'm a college student. There are some category theorists on this website, hopefully they can verify this. But I am almost 100% certain in this case. May18 comment Endomorphic Function Definition Ok, I saw the link. It makes no sense at all. They never say what a surjective morphism is and in general this has no reason to be meaningful in any category. Of course in most examples of categories the morphisms are functions and so of course when talking about functions there is a notion of surjectivity. I am fairly certain that is a mistake. May18 comment Endomorphic Function Definition Where did you read that, do you have a link? May18 comment Endomorphic Function Definition No, an endomorphism is not a surjective morphism on an object to itself. Surjectivity is a property functions have. morphisms are not necessarily functions. The idea I am trying to give you is that categorically speaking we should not care about any properties a morphism has except for its domain, codomain and how it is composed with other morphisms. May18 comment What does “up to a subsequence” mean? Sorry, perhaps I was not clear. Could you provide the source where you first read the phrase that made you want to know what it meant? May18 comment What does “up to a subsequence” mean? Can you post the source? It may help. May17 comment Find the integer x: $x \equiv 8^{38} \pmod {210}$ This is nice. You noticed the order of $8\bmod 105$ is $5$. This technique can sometimes be bad however, this is because if the order is large you will have arrived nowhere. It is safer to use results such as charmicael's lambda and pay the price later having to do a little longer Right-to-left binary method exponentiation. May17 comment Edge that does not appear in ANY spanning tree? +1 for the slick proof. May17 comment Edge that does not appear in ANY spanning tree? Oh, a loop. Of course. May17 comment Closed form of S(n): Oh, that is a really nice way to see it Alexey Burdin. May17 comment Closed form of S(n): Oh I see, I will try :). Very nice problem. May17 comment Closed form of S(n): wait, you already knew the solution? May17 comment Find the integer x: $x \equiv 8^{38} \pmod {210}$ Nice,clear and concise. This is the idea behind Carmichael lambda is it not? May17 comment Find the integer x: $x \equiv 8^{38} \pmod {210}$ Sorry, I made a typo in that line. It should say $x\equiv 4 \bmod 5$ May17 comment Closed form of S(n): In fact it turns out no matter how you play the game your score is always going to be $\frac{n(n-1)}{2}$. It's impossible to do better or worse. May17 comment Closed form of S(n): In fact can you find a way to split them up that gives a number different than $28$? May17 comment Closed form of S(n): Do you have a counterexample? May17 comment Closed form of S(n): When starting with $8$ blocks and using my method you get a score of $28$ May17 comment Closed form of S(n): I think the best strategy is always dividing stacks as equally as possible.