4
votes
Accepted
Creative Algebra Net Problem Solving Question
Since you have $4$ linear equations in $3$ unknowns, it's an overdetermined system and, thus, potentially inconsistent, but this answer shows this isn't the case. First, to avoid dealing with ...
- 49.7k
4
votes
Accepted
Solutions to $(f(x)-f(y))^3=f\left(x^3\right)-f\left(y^3\right)$
I leave my proof, let me know if there are some incorrect reasonings please.
The globally constant functions satisfy our equation, so we can suppose there are $x$ and $y$ such that $f(x)\neq f(y)$. We ...
- 8,911
3
votes
Accepted
Tetrahedron analogue of a triangle Cevians property
First, a proof for equation $(1)$ will be given. Then, an analogous method will be employed for the case of a tetrahedron.
Part 1: Proof for $(1)$
For a triangle $\triangle XYZ$, let $[XYZ]$ denote ...
- 1,275
2
votes
Are there infinitely many numbers for which there is no power of 3 with the hamming weight of its binary representation equal to that number?
A011754 is the sequence of Hamming weights of $3^n$. It states:
Senge & Straus prove that for every $m$, there is some $N$ such that for all $n > N$, $a(n) > m$. Dimitrov & Howe make ...
- 17k
1
vote
Seeking "900 Geometry Problems" Book – Any Leads on Its Whereabouts?
I think you heard it a little wrong.
The title is "110 Geometry Problems for the International Mathematical Olympiad" authored by Titu Andreescu & Cosmin Pohoata
Check out :
https://www....
- 12.3k
1
vote
Accepted
Number of ways to place $4$ kings on an $n \times n$ chessboard
Here is a formula for case 2.
Strategy: for each polyplet of size 4 (polyomino connected at edges or corners) (up to rotation and symmetry), count the number of translations of that polyplet in the ...
- 4,835
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