MathDB

2

Part of 2008 Turkey MO (2nd round)

Problems(2)

prime p and perfect square

Source: Turkey NMO 2008 Problem 2

12/2/2008
a \minus{} ) Find all prime p p such that \dfrac{7^{p \minus{} 1} \minus{} 1}{p} is a perfect square b \minus{} ) Find all prime p p such that \dfrac{11^{p \minus{} 1} \minus{} 1}{p} is a perfect square
quadraticsnumber theory
Intersection set of circles

Source: Turkey NMO 2008 Problem 5

12/2/2008
A circle Γ \Gamma and a line ℓ \ell is given in a plane such that ℓ \ell doesn't cut Γ \Gamma.Determine the intersection set of the circles has [AB] [AB] as diameter for all pairs of {A,B} \left\{A,B\right\} (lie on ℓ \ell) and satisfy P,Q,R,S∈Γ P,Q,R,S \in \Gamma such that PQ \cap RS\equal{}\left\{A\right\} and PS \cap QR\equal{}\left\{B\right\}
geometrysymmetrygeometry unsolved