Compatibility of equations with truncated Newton's binomials
  The resolvability of equations in integers containing truncated Newton's binomial, is determined by the divisibility of the binomial by the characteristic parameters of the equation, which most often is the binomial exponent. Two types of equations containing binomials from two and three integers are investigated. Conditions of resolvability of the equations are specified based on the characteristics of their parameters. 
Anatoly A. Grinberg
math.GM