MathDB

2

Part of 1995 South africa National Olympiad

Problems(2)

Prove that this angle is right

Source: South African MO 1995 Q2

5/27/2012
ABCABC is a triangle with A^<C^\hat{A}<\hat{C}, and DD is the point on BCBC such that BA^D=AC^BB\hat{A}D=A\hat{C}B. The perpendicular bisectors of ADAD and ACAC intersect in the point EE. Prove that BA^E=90āˆ˜B\hat{A}E=90^\circ.
geometrycircumcirclegeometry unsolved
n divides m^2+1 and m divides n^2+1

Source: South African MO 1995 Q6

5/27/2012
Find all pairs (m,n)(m,n) of natural numbers with m<nm<n such that m2+1m^2+1 is a multiple of nn and n2+1n^2+1 is a multiple of mm.
algebrapolynomialVietafunctionnumber theory unsolvednumber theory