What is the smallest integer multiple of 9997,other than 9997 itself,which contains only odd digits?

Maria Jose.

Let's consider 9997n. First note that n must be odd. Then, because 9997=10000-3, if n £ 3333 then 3n < 10000 and so 9997n looks like

[n-1][10000-3n]

that is, the first few digits of 9997n are the number (n-1) and the remaining digits are the number (10000-3n) (with leading zeros if necessary). But since n is odd, the last digit of n-1 is even, so that's no good.

So n > 3333, and trying the first odd values of n greater than 3333 (i.e. 3335) works.

James.