Arithmetic combinatorics is the study of combinatorial estimates associated with arithmetic operations. It lies in the intersection of harmonic analysis, combinatorics, ergodic theory, and number theory. This tag is for questions related to arithmetic combinatorics.
Questions tagged [arithmetic-combinatorics]
52 questions
26
votes
3 answers
Arithmetic Progressions in slowly oscillating sequences
An infinite sequence ($a_0$, $a_1$, ...) is such that the absolute value of the difference between any 2 consecutive terms is equal to $1$. Is there a length-8 subsequence such that the terms are equally spaced on the original sequence and the terms…
user198454
2
votes
1 answer
Numbers not of the form $x^2+My^2$
Why are there only 436 numbers not of the form $x^2+My^2$ for $x>0$, $y>1$ and $M>0$?
This is A074885 from OEIS. The last number is 1875902.
Can the following argument be fixed up?
I expect $N$ to be a quadratic residue $\mod p$
for about half…
Empy2
- 50,853
0
votes
1 answer
Combinations problem with 2 contradicted answers!
If I have the digits from $0$ up till $9$: $0,1,2,3,\cdots,9$. How many 3-digit number can be made from these set of digits if the number is greater than $600$?
My solution was as follows:There are $4$ ways to choose the first digit $(6,7,8,9)$,…
M.Samuel
- 215
-2
votes
1 answer
Integers Placed On A Circle
My problem is such:
On a circle there are $9$ distinct positive integers aranced in such a way that the product of two non-adjacent numbers in the circle is a multiple of $n$ and the product of any two adjacent numbers in the circle is not a…
Rick Shawn
- 29