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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?
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If $ABBA-BAAB=A-B$, show $\operatorname {tr} (A^2)=\operatorname...
Jan 26, 2026 · That is, there seems to be fairly strong symbolic evidence that for $n=4$, if $ABBA-BAAB = A-B$ and $A$ is nilpotent, then $B^4 = \lambda I$ for some $\lambda$.
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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 the same as...
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Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange
There must be something missing since taking $B$ to be the zero matrix will work for any $A$.
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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).
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How to calculate total combinations for AABB and ABBB sets?
Apr 19, 2022 · Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB...), where order matters and repetition is allowed, both can be rearranged in different ways: First one: AABB, BBAA,
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How many $4$-digit palindromes are divisible by $3$?
Feb 28, 2018 · Hint: in digits the number is $abba$ with $2 (a+b)$ divisible by $3$.
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$A^2=AB+BA$. Prove that $\\det(AB-BA)=0$ - Mathematics Stack...
I get the trick. Use the fact that matrices "commute under determinants". +1
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prove $\\Gamma(a)\\Gamma(b) = \\Gamma(a+b)B(a,b)$ using polar ...
Jun 23, 2022 · Are you required to make it wiht polar transformation? Because with the change $x=uv$ $y=u (1-v)$ it's easier
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elementary number theory - Divisibility Tests for Palindromes ...
I've found and proven the following extensions to palindromes of the usual divisibility rules for 3 and 9: A palindrome is divisible by 27 if and only if its digit sum is. A palindrome is divisible by 81 if and only i...