Question

Aflati x si y din:xy+2008y^2=2009 in Z

Answer 1

2008 y² + xy = 2009 => y² =1 si xy = 1

y₁ = 1 => x₁ = 1 => 2008 + 1 = 2009

y₂ = -1 => x₂ = -1 <=> 2008 (-1)² + (-1)(-1) = 2008+1 = 2009

Alte solutii:

y₃ = 7 => x₃ = 13769 ; 2008*49 + 7x =2009 => x = (98392-2009)/7 =

x = 96383/7 = 13769

y₄ = -7 => x₄ = -13769

y₅ = 41 => x₅ = 82279 ; 2008*1681 + 41x = 2009 =>

x = (3375448-2009)/41 = 3373439/41 = 82279

y₆=-41 => x₆ = -82279

y₇ = 49 => x₇ = 98351 ; 2008*2401+49x = 2009

=> x = (4821208-2009)/49 = 4819199/49 = 98351

y₈=-49 => x₈ = -98351

y₉ = 287 => x₉ = 576289 ; 2008*82369+287x =2009 =>

x = (165396952-2009)/287 = 165394943/287= 576289

y₁₀=-287 => x₁₀ = -576289