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Problem 6 (due Monday, April 24)

Non-negative integers $d_i$, $i\in \mathbb Z$, satisfy the following condition: \[d_k=|\{i<k: d_i+i\geq k\}|\] for every integer $k$. Prove that there is a positive integer $n$ such that \[ d_k\in \{n-1,n\}\ \ \text{and}\ \ d_{k+n}=d_k\] for every integer $k$.

Only one solution was submitted, by Prof. Vladislav Kargin. His solution is different from our original solution. For details see the following link Solution.

pow/problem6s23.txt · Last modified: 2023/05/03 03:08 by mazur