Question

A^2 - b^2 = 2019 i need the answer to win a two dollar bet. both integers have to be positive

Answer 1

$Use\ a^2-b^2=(a-b)(a+b).\\\\a^2-b^2=2109\\\\(a-b)(a+b)=2019\\\\(a-b)(a+b)=3\cdot673\to a-b=3\ \wedge\ a+b=673\\\\\underline{+\left\{\begin{array}{ccc}a-b=3\\a+b=673\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2a=676\qquad\text{divide both sides by 2}\\.\qquad\boxed{a=338}\\\\\text{Put the value of a to the second equation}\\\\338+b=673\qquad\text{subtract 338 from both sides}\\\\\boxed{b=335}\\\\Answer:\ \boxed{a=338\ and\ b=335}$