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May
18
comment Prove or disprove: If $a^2 \mid bc$, then $a \mid b$ or $a \mid c$
Sure, happy to help.
May
18
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.
May
18
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.
May
18
comment Endomorphic Function Definition
Where did you read that, do you have a link?
May
18
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.
May
18
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?
May
18
comment What does “up to a subsequence” mean?
Can you post the source? It may help.
May
17
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.
May
17
comment Edge that does not appear in ANY spanning tree?
+1 for the slick proof.
May
17
comment Edge that does not appear in ANY spanning tree?
Oh, a loop. Of course.
May
17
comment Closed form of S(n):
Oh, that is a really nice way to see it Alexey Burdin.
May
17
comment Closed form of S(n):
Oh I see, I will try :). Very nice problem.
May
17
comment Closed form of S(n):
wait, you already knew the solution?
May
17
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?
May
17
comment Find the integer x: $x \equiv 8^{38} \pmod {210}$
Sorry, I made a typo in that line. It should say $x\equiv 4 \bmod 5$
May
17
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.
May
17
comment Closed form of S(n):
In fact can you find a way to split them up that gives a number different than $28$?
May
17
comment Closed form of S(n):
Do you have a counterexample?
May
17
comment Closed form of S(n):
When starting with $8$ blocks and using my method you get a score of $28$
May
17
comment Closed form of S(n):
I think the best strategy is always dividing stacks as equally as possible.