The three solutions are:
- [tex] a = 1,\ b = 3 [/tex]. In fact, [tex] 1+333+333+333 = 1333 [/tex]
- [tex] a = 2,\ b = 6 [/tex]. In fact, [tex] 2+666+666+666+666 = 2666 [/tex]
- [tex] a = 3,\ b = 9 [/tex]. In fact, [tex] 3+999+999+999+999 = 3999 [/tex]
You can find the first one with a bit of trial and error. The second and third derive from the fact that if you multiply by 2 or 3 every term, the whole result will be multiplied by 2 or 3 as well
