MathDB

4

Part of 2001 Bundeswettbewerb Mathematik

Problems(2)

Segment AB has no common point with the square R

Source: Germany Bundeswettbewerb Mathematik 2001, Round 2, Problem 4

1/17/2004
A square R R of sidelength 250 250 lies inside a square Q Q of sidelength 500 500. Prove that: One can always find two points A A and B B on the perimeter of Q Q such that the segment AB AB has no common point with the square R R, and the length of this segment AB AB is greater than 521 521.
geometryperimeterrotationalgebrafunctiondomaingeometry unsolved
Nb. of divisors whose dec. representations ends with 1 or 9

Source: Germany Bundeswettbewerb Mathematik 2001, Round 1, Problem 4

2/1/2009
Prove: For each positive integer is the number of divisors whose decimal representations ends with a 1 or 9 not less than the number of divisors whose decimal representations ends with 3 or 7.
number theoryprime factorizationprime numbersnumber theory unsolved