MathDB

2

Part of 2009 Rioplatense Mathematical Olympiad, Level 3

Problems(2)

Nine points, three pentagons, and one triangle in space

Source: XVIII Olimpíada Matemática Rioplatense (2009)

7/23/2011
Let AA, BB, CC, DD, EE, FF, GG, HH, II be nine points in space such that ABCDEABCDE, ABFGHABFGH, and GFCDIGFCDI are each regular pentagons with side length 11. Determine the lengths of the sides of triangle EHIEHI.
trigonometrygeometrycircumcircleparallelogramgeometry unsolved
Find all (a,b) with a divides b+1 and b divides a^3-1

Source: XVIII Olimpíada Matemática Rioplatense (2009)

7/23/2011
Find all pairs (a,b)(a,b) of integers with a>1a>1 and b>1b>1 such that aa divides b+1b+1 and bb divides a3−1a^3-1.
number theory unsolvednumber theory