MathDB

1

Part of 2011 239 Open Mathematical Olympiad

Problems(2)

a+b=b(a-c), c+1 square of prime, then a+b of ab square

Source: 239 2011 J2

5/17/2020
Positive integers a,b,ca,b,c satisfy that a+b=b(aāˆ’c)a+b=b(a-c) and c+1 is a square of a prime. Prove that a+ba+b or abab is a square.
number theory
2AP=BC, X,Y symmetric to P, find C

Source: 239 2011 J1

5/17/2020
In the acute triangle ABCABC on ACAC point PP is chosen such that 2AP=BC2AP=BC. Points XX and YY are symmetric to PP wrt AA and CC respectively. It turned out that BX=BYBX=BY. Find angle CC.
geometry