23 11 Article 08.2.4 Journal of Integer Sequences, Vol. 11 (2008), 2 3 6 1 47 Unimodal Rays in the Ordinary and Generalized Pascal Triangles Hac` ene Belbachir 1 USTHB, Faculty of Mathematics P.O. Box 32 El Alia, Algiers Algeria hbelbachir@usthb.dz hacenebelbachir@gmail.com L´aszl´oSzalay 2 Institute of Mathematics and Statistics University of West Hungary Erzs´ ebet utca 9 H-9400 Sopron Hungary laszalay@ktk.nyme.hu Abstract The present paper provides the solution of two problems recently posed by Bencherif, Belbachir and Szalay. For example, they conjectured that any sequence of binomial coefficients lying along a ray in Pascal’s triangle is unimodal. 1 Research supported by LAID3 Laboratory of USTHB University and by TASSILI CMEP Accord 05 MDU641b. 2 Research supported by a J´ anos Bolyai Scholarship of HAS, and by Hungarian National Foundation for Scientific Research Grant No. T 048954 MAT, No. T 61800 FT. 1