부산대학교 도서관

We investigate Diophantine problems concerning linear combinations of polynomials of the shape a 0 x + a 1 x (x + 1) + a 2 x (x + 1) (x + 2) + ⋯ + a n x (x + 1) ... (x + n) with n ∈ N ∪ { 0 } . We provide effective finiteness results for the power, shifted power, and quadratic polynomial values of these linear combinations, generalizing the analogous results of Hajdu, Laishram and Tengely [10], and of Bérczes, Hajdu, Luca and the author [2] given for the sums x + x (x + 1) + x (x + 1) (x + 2) + ⋯ + x (x + 1) ... (x + n) , i.e., for the case a 0 = a 1 = ⋯ = a n = 1 . Our work is closely connected also with some results of Tengely and Ulas [15] concerning the case when the coefficients a 0 , a 1 , ... , a n are zeroes and ones. [ABSTRACT FROM AUTHOR]