Question

Daca 5 divide pe (ab+3), atunci suma valorilor numarului ab este:

Answer 1

ab+3=M5
10a+(b+3)=M5, rezulta 
b+3=5, b=2
b+3=10, b=7

Suma=12+17+22+27+32+37+42+47+52+57+62+67+72+77+82+87+92+97=
=(12+22+...+92)+(17+27+...+97)=[12+(12+10)+(12+20)+...+(12+80)]+
+[17+(17+10)+(17+20)+...+(17+80)]=
=[9x12+(10+20+...+80)]+[9x17+(10+20+...+80)]=
=9x(12+17)+2(10+20+...+80)=9x29+20(1+2+...+8)=261+20x8x9/2=
=261+720=981