Reused R values

[isarac3]

If two different bitcoin addresses use the same r value in different transaction, Does it mean that the k value is the same?

[o_e_l_e_o]

Yes. The private key or public key of the address in question play no part in the computation of the r value.

The r value is simply defined as the x coordinate (mod n) of the point kG, with G being the generator point of the curve. r is essentially the x coordinate of the public key to the private key k.