Question

Hallar “a + b + c” si se cumple que
m1m+m2m+...+m3m+m8m=abc2

Answer 1

$\overline{m1m}+\overline{m2m}+\cdots+\overline{m8m}=\overline{abc2}\\\\(100m+10+m)+(100m+20+m)+\cdots + (100m+80+m)=\overline{abc2}\\\\(101m+10)+(101m+20)+\cdots+(101m+80)=\overline{abc2}\\\\808m+360=\overline{abc2}\\\\\text{Entonces }m\in\{4,9\}\\\\\text{Si }m=4: 3232+360=3292=\overline{abc2}\\\\\text{Si }m=9: 7272+360=7632=\overline{abc2}$

(a,b,c) ∈ {(3,2,9),(7,6,3)}

a+b+c ∈ {14 , 16}