Question

por favor alguien? no me sale

Answer 1

$\overline{abab}_{8}=\overline{mn0n}_{7}\\ \\ 8^3a+8^2b+8a+b=7^3m+7^2n+n\\ \\ 8a(8^2+1)+b(8^2+1)=7^3m+50n\\ \\ 65(8a+b)=7^3m+50n\\ \\ \textcircled{1}: 5~|~7^3m+50n\Rightarrow m\in\{0,5.10,15,...\}\wedge m\in[1,6]\Rightarrow \boxed{m=5}\\ \\ \\ 13(8a+b)=7^3+10n\\ \\ \textcircled{2}:7^3+10n\equiv 0\mod 13\\ \\ 5+10n\equiv 0\mod 13\\ \\ 1+2n\equiv 0\mod 13\\ \\ \boxed{n=6}\\ \\ \\ \text{Entonces }\overline{abab}_{8}=5606_7=2015=3737_8\\ \\ \\ a+b+m+n=3+7+5+6\\ \\ \boxed{a+b+m+n=21}$