All Questions
37
questions
0
votes
1
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315
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Understanding Ziv's proof of zero sum problem .
I was going through the proof of zero sum problem in one dimension as provided by Abraham Ziv. The problem statement is to prove that given a set of $2n+1$ integers, we can find at least $n$ integers ...
- 325
0
votes
0
answers
138
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Contradiction in Frobenius coin problem
The Frobenius coin problem guarantees that if $(a,b)=1$, then
$$ax+by$$ does not represent exactly $(a-1)(b-1)/2$ numbers all below $ab-a-b$ if $x,y\geq0$ holds.
I am confused by following argument.
...
- 6,245
2
votes
1
answer
746
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Questions on Erdős–Ginzburg–Ziv theorem for primes and understanding related lemmas and their applications.
While trying to prove the prime case of Erdős–Ginzburg–Ziv theorem:
Theorem: For every prime number $p$, in any set of $2p-1$ integers, the sum $p$ of them divisible by $p$.
I came across with ...
- 6,810
1
vote
0
answers
87
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Simple $\{-1,0,1\}$ equation set
I'm trying to find the shortest path, getting from $x=0$ to $x=k$ in a certain problem, where I can slowly accelerate and decelerate.
It comes down to finding the smallest $n$ and set of values $\{...
- 4,814
6
votes
2
answers
640
views
Number-Theoretic Coin Puzzle
There are three piles of coins. You are allowed to move coins from one pile to another, but only if the number of coins in the destination pile is doubled. For example, if the first pile has 6 coins ...
- 899
6
votes
1
answer
403
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Show there’s at most $n\choose \left \lfloor\frac{n}{2} \right\rfloor$ subsets $A\subset[n]$ such that $\displaystyle\sum\limits_{i\in{A}} a_i=\alpha$
Let $a_1, a_2, a_3, ... , a_n$ and $\alpha$ be n+1 non-zero real numbers. Prove that there are at most $n\choose \left\lfloor\frac{n}{2}\right\rfloor$ subsets $A\subset[n]$ such that $\displaystyle\...
- 195
5
votes
1
answer
460
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Arithmetic progressions
What are the largest known lower bounds for $B_k$, the maximal sum of the reciprocals of the members of subsets of the positive integers which contain no arithmetic progressions of length $k$?
for $k=...
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