MathDB

24

Part of 2020 BMT Fall

Problems(2)

2020 BMT Team 24

Source:

1/9/2022
For positive integers NN and mm, where m≤Nm \le N, define am,N=1(N+1m)∑i=m−1N−1(im−1)N−ia_{m,N} =\frac{1}{{N+1 \choose m}} \sum_{i=m-1}^{N-1} \frac{ {i \choose m-1}}{N - i} Compute the smallest positive integer NN such that ∑m=1Nam,N>2020NN+1\sum^N_{m=1}a_{m,N} >\frac{2020N}{N +1}
algebracombinatorics
2020 BMT Individual 24

Source:

1/9/2022
Let NN be the number of non-empty subsets TT of S={1,2,3,4,...,2020}S = \{1, 2, 3, 4, . . . , 2020\} satisfying max⁡(T)>1000\max (T) >1000. Compute the largest integer kk such that 3k3^k divides NN.
number theory