MathDB

1

Part of 2003 Italy TST

Problems(2)

a B,I,G problem

Source: Italy TST 2003

11/9/2010
The incircle of a triangle ABCABC touches the sides AB,BC,CAAB,BC,CA at points D,E,FD,E,F respectively. The line through AA parallel to DFDF meets the line through CC parallel to EFEF at GG. (a)(a) Prove that the quadrilateral AICGAICG is cyclic. (b)(b) Prove that the points B,I,GB,I,G are collinear.
geometrygreatest common divisorcircumcirclegeometry unsolved
Diophantine - Find all (a,b,p)

Source: Italy TST 2003

11/9/2010
Find all triples of positive integers (a,b,p)(a,b,p) with a,ba,b positive integers and pp a prime number such that 2a+pb=19a2^a+p^b=19^a
modular arithmeticnumber theory proposednumber theory