关于丢番图方程x2+by=cz

设s,t满足gcd(s,t)=1,s>t的正整数,a=2st,b=s~2-t~2,c=s~2+t~2。证明了:若c为素数幂且满足下列条件之一:(1)b有因子b_1≡±5(mod8),(2)b≡-1(mod8),(3)5|c。则不定方程x~2+b~y=c~z仅有一组正整数解(x,y,z)=a,2,2。     

How useful are the demographic surveys in explaining the determinants of early marriage of girls in the Terai of Nepal?

In recent decades significant changes in Nepalese society have greatly contributed to the increase in age at marriage of girls in Nepal. Factors responsible for these changes include educational development, urbanization and development of mass communications. However, many parents still marry their daughters at very young ages and this practice is particularly prevalent in the Terai region. This paper examines several demographic data sets with a view to assessing their utility for understanding the determinants of early age of marriage of girls in the Terai. The Nepal Family Health Survey (1996), Nepal Demographic and Health Surveys (2001, 2006), the Nepal Adolescents and Young Adults Survey (1999) and the 2001 Population Census of Nepal describe changes in at marriage over time. Factors such as sex, religion, education, geographic region, place of residence (rural/urban), economic status of the household and of women, and occupation are included in these data sets. However, other factors such as age at menarche, dowry and cost of marriage and cross-border marriage migration, which have been found to affect the prevalence of the lower age at marriage of girls in the Terai region, have not been included in the existing demographic surveys. Findings from the current study suggest that these variables should be included in future demographic surveys.