本文研究了数列A(D)中三角数的存在性问题.利用Pell方程和Petr方程的解的性质,得到了数列A(D)含有三角数的三个必要条件,并证明了当D≤20时,数列A(D)仅当D=2,11,14时含有三角数.推广了Prasad与Rao[3]和罗明[4]的结果.%The aim of this paper is to study the existence of the triangular numbers in sequences A(D). By using the properties of Pell equation and Petr equation, Three necessary conditions for A(D) contains triangular numbers are given. Moreover, we proved that, for D ≤ 20, the sequence A(D) contains triangular numbers if and only if D = 2,11 and 14, and generalize the results of Prasad[3] and Luo[4].
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