Question

cel mai mic numar natural >1970 cre inpartit la 2 ; 20; 25; sa dea resturile 1; 19; 24

Answer 1

$x=2*c _{1} +1 ;c _{1} \geq 985\\ x=20*c _{2} +19 ;c _{2} \geq 98\\ x=25*c _{3} +24 ;c _{3} \geq 78\\ \\ 2*c _{1} +1 =20*c _{2} +19 =25*c _{3} +24 \\ \\ 2*c _{1} +1=20*c _{2}+19\\ 2*c _{1} -20*c _{2}=19-1 \\2(c _{1} -10*c _{2})=18\\ c _{1} -10*c _{2}=9\\ \\ 20*c _{2} +19 =25*c _{3} +24 \\ 20*c _{2} -25*c _{3}=24-19 \\ 20*c _{2} -25*c _{3}=5 \\ 4*c _{2}-5*c _{3}=1 \\ \\ c _{2}=99 \\ c _{3}=79 \\ c _{1}=9 \\ x=1999$