N is a positive integer ending in 5 – that is, positive integers like 2015, 21335, 349705 etc.

Under what conditions do gcd(N, floor(N²/100)) exceed 1?

(For example, if N = 2015, then floor(N²/100) = 40602, so that:
gcd (N, floor(N²/100)) = 1, which contravenes the provisions of the problem.)