Let a and b given unequal positive integers; it is desired to determine the positive integer solutions n and x of the equation
of the title. Some special cases have recently been considered, and here some general results and conjectures are presented.
Total body neutron activation analysis (TBNAA) has used to determine the absolute levels of total body sodium (TBNa) and total
body chlorine (TBCl) in 81 normal adults. For the age span studied (30–90 years), the mean values of TBNa and TBCl remained
relatively constant for males, but decreased slightly for females beyond sixty years of age. In order to reduce the variability
in this cross-sectional study, the TBNa and TBCl values were normalized for body dimensions (weight, height, body surface
area) as well as age and sex. In addition, TBNa was related to skeletal mass (total body calcium) and lean body mass (total
body potassium). The quantity of body sodium in excess of the chlorine space was determined. This value, defined as sodium
excess, was significantly correlated with total body calcium. The values for total body sodium, total body chlorine, and sodium
excess obtained in the present study were compared with values previously reported in the literature.