MathDB

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Part of 2023 Assara - South Russian Girl's MO

Problems(2)

< AXC=? AC = BD, <ABX = <AX B = 50^o, <CAD = 51^o, <AED = 80^o

Source: 2023 South Russian Girls MO - Assara Juniors p2

2/28/2024
In the convex quadrilateral ABCDABCD, point XX is selected on side ADAD, and the diagonals intersect at point EE. It is known that AC=BDAC = BD, ∠ABX=∠AXB=50o\angle ABX = \angle AX B = 50^o, ∠CAD=51o\angle CAD = 51^o, ∠AED=80o\angle AED = 80^o. Find the value of angle ∠AXC\angle AXC.
geometrysngles
a^a is divisible by b^b

Source: 2023 South Russian Girls MO - Assara Seniors p2

3/1/2024
The natural numbers aa and bb are such that aaa^a is divisible by bbb^b. Can we say that then aa is divisible by bb?
number theorydivisibledivides