MathDB

16

Part of 2013 Baltic Way

Problems(1)

Delightful Integers

Source: 2013 Baltic Way, Problem 16

12/31/2013
We call a positive integer nn delightful if there exists an integer kk, 1<k<n1 < k < n, such that 1+2+⋯+(k−1)=(k+1)+(k+2)+⋯+n1+2+\cdots+(k-1)=(k+1)+(k+2)+\cdots+n Does there exist a delightful number NN satisfying the inequalities 20132013<N20132013<20132013+4?2013^{2013}<\dfrac{N}{2013^{2013}}<2013^{2013}+4 ?
inequalitiesnumber theory unsolvednumber theory