
How many $4$-digit palindromes are divisible by $3$?
Feb 28, 2018 · How many 4 4 -digit palindromes are divisible by 3 3? I'm trying to figure this one out. I know that if a number is divisible by 3 3, then the sum of its digits is divisible by 3 3. All I have done …
Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange
As long as a, b, c a, b, c are not all 0 0, this has rank 2 2, so there is a 2 2 -dimensional linear space of B B for which AB + BA = 0 A B + B A = 0 in this case. On ...
measure theory - $L^2$ bounded implies uniformly integrable ...
Aug 24, 2020 · It's more basic than that: a family of random variables which is bounded in $L^2$ is uniformly integrable (see here).
11 | abba, where a and b are the digits in a 4 digit number.
Nov 21, 2013 · Truly lost here, I know abba could look anything like 1221 or even 9999. However how do I prove 11 divides all of the possiblities?
How many ways can we get 2 a's and 2 b's from aabb?
Because abab is the same as aabb. I was how to solve these problems with the blank slot method, i.e. _ _ _ _. If I do this manually, it's clear to me the answer is 6, aabb abab abba baba bbaa baab Which is …
How to show that $A^2=AB+BA$ implies $\det (AB-BA)=0$ for …
Jan 26, 2015 · Let $A$ and $B$ be two $3\times 3$ matrices with complex entries such that $A^2=AB+BA$. Prove that $\det (AB-BA)=0$. (Is the above result true for matrices with real ...
sequences and series - The Perfect Sharing Algorithm (ABBABAAB ...
Oct 4, 2016 · The algorithm is normally created by taking AB, then inverting each 2-state 'digit' and sticking it on the end (ABBA). You then take this entire sequence and repeat the process (ABBABAAB).
CW complex for Möbius strip and its homeomorfisams
Jan 14, 2023 · According to this question, there is CW complex with one 0-cell,one 1-cell and one 2-cell. No such CW structure exists on the the Möbius strip. Moreover the linked question doesn't claim that, …
matrices - Reducing matrix multiplication to squaring - Mathematics ...
Sep 20, 2022 · I'm trying to solve problem 4.2-6 in the fourth edition of CLRS: Suppose that you have a $\\Theta(n^\\alpha)$-time algorithm for squaring $n \\times n$ matrices ...
elementary number theory - Common factors for all palindromes ...
For example a palindrome of length $4$ is always divisible by $11$ because palindromes of length $4$ are in the form of: $$\\overline{abba}$$ so it is equal to $$1001a+110b$$ and $1001$ and $110$ are