1) x³-y³=(x-y)(x²+xy+y²)
(x-y)(x²+xy+y²)=2044
(x-y)(x²+xy+y²)=2²·7·73
[tex]\left \{ {{x-y=1} \atop {x^2+xy+y^2=2044}} \right.[/tex]
[tex]\left \{ {{x-y=2} \atop {x^2+xy+y^2=1022}} \right. \left \{ {{x-y=4} \atop {x^2+xy+y^2=511}} \right. \left \{ {{x-y=7} \atop {x^2+xy+y^2=292}} \right. \left \{ {{x-y=14} \atop {x^2+xy+y^2=146}} \right. \left \{ {{x-y=28} \atop {x^2+xy+y^2=73}} \right.[/tex]
[tex]\left \{ {{x-y=73} \atop {x^2+xy+y^2=28}} \right. \left \{ {{x-y=146} \atop {x^2+xy+y^2=14}} \right. \left \{ {{x-y=292} \atop {x^2+xy+y^2=7}} \right. \left \{ {{x-y=511} \atop {x^2+xy+y^2=4}} \right.\left \{ {{x-y=1022} \atop {x^2+xy+y^2=2}} \right.[/tex]
[tex]\left \{ {{x-y=2044} \atop {x^2+xy+y^2=1}} \right.[/tex]
и
[tex]\left \{ {{x-y=-1} \atop {x^2+xy+y^2=-2044}} \right.[/tex]
[tex]\left \{ {{x-y=-2} \atop {x^2+xy+y^2=-1022}} \right. \left \{ {{x-y=-4} \atop {x^2+xy+y^2=-511}} \right. \left \{ {{x-y=-7} \atop {x^2+xy+y^2=-292}} \right. \left \{ {{x-y=-14} \atop {x^2+xy+y^2=-146}} \right. \left \{ {{x-y=-28} \atop {x^2+xy+y^2=-73}} \right.[/tex]
[tex]\left \{ {{x-y=-73} \atop {x^2+xy+y^2=-28}} \right. \left \{ {{x-y=-146} \atop {x^2+xy+y^2=-14}} \right. \left \{ {{x-y=-292} \atop {x^2+xy+y^2=-7}} \right. \left \{ {{x-y=-511} \atop {x^2+xy+y^2=-4}} \right.\left \{ {{x-y=-1022} \atop {x^2+xy+y^2=-2}} \right.[/tex]
[tex]\left \{ {{x-y=-2044} \atop {x^2+xy+y^2=-1}} \right.[/tex]
Решим эти 24 системы способом подстановки и получим решение системы:
{x-y=4
{x^2+xy+y^2=511
ответ (15;11)
2) xy-11x-11y=1⇒ x(y-11)=1+11y
[tex]x=\frac{11y+1}{y-11}=11+\frac{122}{y-11}[/tex]
y-11 делится на 122 нацело
при y=12;тогда х=133;
при y=13;тогда х=72;
при y=72; тогда x=13
при y=133; тогда х=12
