A Classification of Motzkin Numbers Modulo 8

The well-known Motzkin numbers were conjectured by Deutsch and Sagan to be nonzero when modulo $8$. The conjecture was first proved by Sen-Peng Eu, Shu-chung Liu and Yeong-Nan Yeh by using the factorial representation of the Catalan numbers. We present a short proof by finding a recursive formula for Motzkin numbers modulo $8$. Moreover, such a recursion leads to a full classification of Motzkin numbers modulo $8$. An addendum was added on April 3 2018.

A Factorial Representation of Suicidal Ideation among Academically Gifted Adolescents

Suicidal ideation assessment has been employed as an early screening method for identifying adolescents who are at risk for engaging in suicidal behaviors. While recent evidence has emerged that gifted adolescents do not have a higher rate of suicidal ideation, research on the psychological and personality characteristics of gifted youth have demonstrated that they differ from nongifted students in their mental representations of self. Therefore, this study examined the factorial representation for suicidal ideation among an academically gifted population. The results reveal the structure of suicidal ideation for the gifted sample in this study differs from the established normal sample. Further, the factorial representation outlined for suicidal ideation in the gifted sample supported the suicide trajectory model (Stillion & McDowell, 1996), providing a theoretical base for future intervention and refined assessment.