Question

Calculati suma tuturor numerelor naturale de 3 cifr, care impartite la 31 dau restul 13.

Answer 1

 [tex]numerele\, de\, 3 \,cifre\, se\. incadreaza\,asfel:\,\,\,100\le\overline{abc}\le999/\\ 100:31\approx3\,\,\si\,\,999:31\approx32\\ \Rightarrow\,\,\overline{abc}=\{3*31+13=106\,,\,4*31+13=137\,,\,...\,31*31+13=974\}\\ S=106+137+...+974=\\ =106+(106+1*31)+(106+2*31)+...+(106+28*31)=\\ =106*(28+1)+28*31=3074+868=3942[/tex]