T-cobalancing and lucas t-cobalancing numbers

In this thesis, the general terms of all t-cobalancing numbers, Lucas t-cobalancing numbers and t-cobalancers are determined. In the first section, some notations and definitions on balancing and cobalancing numbers are given. Further some new results obtained recently on balancing numbers and cobalancing numbers are given. In the second section, general information on Fibonacci, Lucas, Pell and Pell-Lucas integer sequences are given. In the third section, the material and method are given. In the fourth section, which is the original part of the thesis, the general terms of all t-cobalancing numbers, Lucas t-cobalancing numbers and t-cobalancers are given. For this reason, we first determined the set of all positive integer solutions of the Pell equation 2x^2-y^2=2t^2-1 by using its set of representatives. Later we determined the general terms of all t-cobalancing numbers, Lucas t-cobalancing numbers and t-cobalancers. The problem is considered in three cases: t=1 and 2t^2-1 is a perfect square or not for t≥2. In the last section, result is given.