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Apr
21
comment Annihilators for an expression
What exactly is that formula? What do you mean by "annihilator"?
Apr
20
comment Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
@YilunZhang Yes, which is quite easy. The standard proof is on the wiki article I linked.
Apr
20
comment Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
@YilunZhang What do you mean? I'm just applying the well known recursive identity for binomial coefficients.
Apr
20
answered Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
Apr
20
revised denumerables: prove or disprove the following
edited tags
Apr
20
comment denumerables: prove or disprove the following
I think it's best if you explain your answers. An answer like this simultaneously encourages no-effort homework questions, and serves no lasting purpose for either the question asker or any future readers.
Apr
20
comment What is the period of this sequence?
Trying your formula on the computer, I'm just getting $1$, $p - 1$, $0$, ZeroDivisionError for every value of $p$ I've tried. Are you sure you have it right?
Apr
20
comment How should I try to evaluate this integral?
Is that really a "hint"?
Apr
20
revised Galois field theory
edited tags
Apr
20
awarded  Nice Answer
Apr
20
revised A fascinating number chain.
edited tags
Apr
20
revised A fascinating number chain.
added 162 characters in body
Apr
20
answered A fascinating number chain.
Apr
20
comment A fascinating number chain.
@KarlKronenfeld You're mapping $10x+y$ to $9x+2y$. Look at it modulo $11$. You have $9x+2y=0$, and note that $9=-2$.
Apr
20
comment A fascinating number chain.
I graphed the iteration of your function, and noticed an interesting symmetry. It seems that that the mapping $x\to99-x$ is an "automorphism" for this function: $f(99-x)=99-f(x)$.
Apr
20
comment A fascinating number chain.
@DisplayName The OP just means that you'll eventually enter that chain.
Apr
20
answered Is there any use of this mu function?
Apr
20
comment Getting multiple of 11
Here's a visualization of the iteration of this map over $\mathbb Z_{100}$. It seems there's two cases, some of the numbers just go straight down to $0$ in a big river (and then stay at $0$, of course), while others fall into a whirlpool and cycle forever. Sorry the graph is a bit messy, I couldn't find good layout software.
Apr
20
comment Getting multiple of 11
I don't see how you get $44$ out of $07$.
Apr
20
revised Product of “reversed” numbers
added 2 characters in body