MathDB

3

Part of 2005 Moldova Team Selection Test

Problems(2)

circles and points

Source: Moldova TST 2005

4/9/2005
Does there exist such a configuration of 22 circles and 22 point, that any circle contains at leats 7 points and any point belongs at least to 7 circles?
linear algebramatrixtrigonometrycombinatorics unsolvedcombinatorics
n^k divides [A]

Source: Moldova TST 2005

3/21/2005
A=3∑m=1n2(12−{m})A=3\sum_{m=1}^{n^2}(\frac12-\{\sqrt{m}\}) where nn is an positive integer. Find the largest kk such that nkn^k divides [A][A].
calculusintegrationfunctionnumber theory proposednumber theory