Răspuns: [tex]\boxed{\boxed{\bf a+b+c = 13}}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\bf 2020 : \overline{5a} = \overline{3b}, ~rest~ \overline{2c}[/tex]
[tex]\bf a,b,c - cifre[/tex]
[tex]\bf a,b,c \in\{0,1,2,3,4,5,6,7,8,9\}[/tex]
[tex]\bf \overline{2c} = 2\cdot numar~prim[/tex]
Numerele prime sunt acele numere care au exact doi divizori, numărul 1 și numărul în cauză
Câteva numere prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. ......
[tex]\bf 13\cdot2 = 26\implies \overline{2c}=26\implies c = 6[/tex]
[tex]\bf 11\cdot2 = 22\implies\overline{2c}=22\implies c = 2[/tex]
[tex]\bf 2020 =\overline{3b}\cdot \overline{5a} + \overline{2c}[/tex]
[tex]\bf Daca ~c = 6 \implies 2020 =\overline{3b}\cdot \overline{5a} + 26\implies 2020-26 =\overline{3b}\cdot \overline{5a}[/tex]
[tex]\bf\implies 1994 =\overline{3b}\cdot \overline{5a}\implies 2\cdot 997 =\overline{3b}\cdot \overline{5a}~~~nu~ convine[/tex]
[tex]\bf Daca ~c = 2 \implies 2020 =\overline{3b}\cdot \overline{5a} + 22\implies 2020-22 =\overline{3b}\cdot \overline{5a}[/tex]
[tex]\bf\implies 1998 =\overline{3b}\cdot \overline{5a}\implies 2\cdot 3^{3}\cdot37 =\overline{3b}\cdot \overline{5a}[/tex]
[tex]\bf \implies \overline{3b}=37~~si~~ \overline{5a} = 54\implies\boxed{\bf a = 4~;~b = 7}[/tex]
[tex]\boxed{\bf a = 4;~b = 7;~c=2}[/tex]
[tex]\bf a+b+c = 4+7+2[/tex]
[tex]\boxed{\boxed{\bf a+b+c = 13}}[/tex]
#copaceibrainly
