MathDB

1.3

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

27^n- 2^n is perfect square

Source: 2011 Saudi Arabia Pre-TST November 1.3

1/1/2022
Find all positive integers nn such that 27n−2n27^n- 2^n is a perfect square.
number theoryPerfect Square
4CF<= CB, 4CF = CB => AE is bisector of <DAF, AD=DC=CB<AB, <ADE=<AEF

Source: 2011 Saudi Arabia Pre-TST February 1.3 https://artofproblemsolving.com/community/c2745403_2011_

1/1/2022
The quadrilateral ABCDABCD has AD=DC=CB<ABAD = DC = CB < AB and AB∥CDAB \parallel CD. Points EE and FF lie on the sides CDCD and BCBC such that ∠ADE=∠AEF\angle ADE = \angle AEF. Prove that: (a) 4CF≤CB4CF \le CB. (b) If 4CF=CB4CF = CB, then AEAE is the angle bisector of ∠DAF\angle DAF.
geometric inequalitygeometryangle bisector