Subcontests
(4)interesting sequence
Let (an)n≥1 be a sequence defined by an=2n+49. Find all values of n such that an=pg,an+1=rs, where p,q,r,s are prime numbers with p<q,r<s and q−p=s−r. find all polynomials
Find all polynomials of two variables P(x,y) which satisfy
P(a,b)P(c,d)=P(ac+bd,ad+bc),∀a,b,c,d∈R. another "strange" geometry problem of Bulgaria, but nice
Let ABC be a triangle and let M,N,P be points on the line BC such that AM,AN,AP are the altitude, the angle bisector and the median of the triangle, respectively. It is known that
[ABC][AMP]=41 and [ABC][ANP]=1−23.
Find the angles of triangle ABC.