Multiple contains only digit 9?
Algebra
Level
3
A is an odd number and its last digit isn't 5. Is it possible that A has a multiple which contains only digit 9?
Bonus: Can you prove why this is possible or impossible?
Yes
No
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
For the problem as stated, "is it possible?", yes, of course: eg 9 × 1 = 9 . The more interesting result is that EVERY odd number coprime to 1 0 has a multiple whose digits are all 9 s, and these are closely related to the (recurring) decimal expansions of their reciprocals; for example, 3 7 × 2 7 = 9 9 9 , 7 × 1 4 2 8 5 7 = 9 9 9 9 9 9 .