2

Part of 2007 Pan African

Problems(2)

Locus of points preserving some angles

Source: PAMO 2007 Q2

A

B

C

be three fixed points, not on the same line. Consider all triangles

\angle B'=\angle B

B'

moves on a given straight line (not containing

A

C'

is determined such that

\angle B'=\angle B

\angle C'=\angle C

. Find the locus of

C'

geometry unsolvedgeometry

For which n is this divisible by 2007?

Source: PAMO 2007 Q5

For which positive integers

n

231^n-222^n-8 ^n -1

2007

number theory unsolvednumber theory