Hello, I'm having trouble with a question frmo the British mathematical Olympiad (1997)

N is a four-digit integer which does not end in a zero, and R(n) is the four digit integer obtained by reversing the digits of N. E.g. R(3275)=5723

Determine all such integers N for which R(N)=4N+3

I used the year (1997) as a reference and I found out it does work for the above statement so that's one but I don't know how many others there are.

I've worked out that according to the above statement, R(N) would have to start with either 1,3,5,7 or 9

I've tried laying it out so N=1000a +100b+10c+d and because R(N) must be odd due to +3 it would =4000d+400c+40b+4a and therefore a must be odd, narrowing down the first and last integer of both N and R(N) to be odd.

Now I am stuck. Please help :/