Question

Число 2019 представьте в виде разности квадратов двух натуральных чисел​

Answer 1

$2019=x^2-y^2=(x-y)(x+y)\; \; ,\; \; \; x-y<x+y\\\\2019=1\cdot 2019\; \; \Rightarrow \; \; \; x-y=1\; \; ,\; \; x+y=2019\\\\\left \{ {{x-y=1\quad } \atop {x+y=2019}} \right.\; \; \left \{ {{x-y=1} \atop {2x=2020}} \right.\; \; \left \{ {{y=x-1} \atop {x=1010}} \right.\; \; \left \{ {{y=1009} \atop {x=1010}} \right.\\\\\\\underline {2019=1010^2-1009^2}\\\\ili\\\\2019=3\cdot 673\\\\3\cdot 673=(x-y)(x+y)\\\\\left \{ {{x-y=3} \atop {x+y=673}} \right.\; \; \left \{ {{x-y=3} \atop {2x=676}} \right.\; \; \left \{ {{y=x-3} \atop {x=338}} \right.\; \; \left \{ {{y=335} \atop {x=338}} \right.\\\\\\\underline {2019=338^2-335^2}$