Given square ABCD, on BC's ray choose E (E is outside of BC) , on CD's ray choose F so that DF = BE. Through E draw Ex // À, through F draw Fy // AE. Call intersection of Ex àn Fy is P. Prove that : AEPF is the square . 

Give 2017 positive real numbers a₁ , a₂ , a₃ , a₄ , ............... a₂₀₁₇ so that \(\dfrac{1}{a_1}+\dfrac{1}{a_2}+.....+\dfrac{1}{a_{2017}}=1009\)

Prove that there are at least 2 in 2017 natural numbers on equal .

Give A = 5 + 5² + 5³ + ................ + 5²⁰¹²

Prove that : A \(⋮\) 65