Recently, determining the Ramsey numbers of loose paths and cycles in uniform hyper graphs has received considerable attention. It has been shown that the 2-color Ramsey number of a k-uniform loose cycle C-n(k), R(C-n(k), C-n(k)), is asymptotically 1/2(2k- 1)n. Here we conjecture that for any n >= m >= 3 and k >= 3, R(P-n(k), P-m(k)) = R(P-n(k), C-m(k)) = R(C-n(k), C-m(k)) + 1 = (k-1)n + left perpendicular m+1/2 right perpendicular. Recently the case k = 3 was proved by the authors. In this paper, first we show that this conjecture is true for k = 3 with a much shorter proof. Then, we show that for fixed m >= 3 and k >= 4 the conjecture is equivalent to (only) the last equality for any 2m >= n >= in >= 3. Finally we give a proof for the case m = 3. (C) 2016 Elsevier B.V. All rights reserved.