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“…Beside this, in the study of Stević, we explained some previously obtained formulas for a symmetric system of difference equations obtained from Equation with a = b = 1. These studies, along with an interest in studying symmetric systems of difference equations (see, eg, the studies of Papaschinopoulos) and getting some formulas for solutions to some difference equations obtained by other authors, which are not explained theoretically, have motivated us to conduct considerable investigations of solvability of various difference equations and systems in detail (see, eg, the studies of Stević) and the references therein for some difference equations and systems that are solved by using related methods and ideas to those in the study of Stević. For some other methods for studying solvability of difference equations and systems, including the ones dealing with their invariants, as well as their applications and related topics, see, also the previous studies .…”

confidence: 99%

“…Beside this, in the study of Stević, we explained some previously obtained formulas for a symmetric system of difference equations obtained from Equation with a = b = 1. These studies, along with an interest in studying symmetric systems of difference equations (see, eg, the studies of Papaschinopoulos) and getting some formulas for solutions to some difference equations obtained by other authors, which are not explained theoretically, have motivated us to conduct considerable investigations of solvability of various difference equations and systems in detail (see, eg, the studies of Stević) and the references therein for some difference equations and systems that are solved by using related methods and ideas to those in the study of Stević. For some other methods for studying solvability of difference equations and systems, including the ones dealing with their invariants, as well as their applications and related topics, see, also the previous studies .…”

confidence: 99%

“…Since that time, related transformations have been frequently used on difference equations ( [14][15][16]), as well as on close to symmetric systems (see [15,17,18] and numerous references therein), an area essentially initiated by Papaschinopoulos and Schinas (see [19][20][21][22][23][24][25]). Somewhat more complex methods can be found in [26]. For some related topics, such as finding invariants, special types of solutions and applications of solvable difference equations (see, for example, [21][22][23]25,[27][28][29] and the references therein).…”

confidence: 99%

“…where coefficients (a n ) n∈N , (b n ) n∈N , and the initial value x 0 are real or complex (see [11][12][13][14][15]17,18,26,30]), which shows how useful the equation is (for how Equation (4) is solved, consult, for example, [3,8]; the book [3] has a nice explanation of three methods for solving it). Recently, we have studied several classes of product-type equations and systems (see [31][32][33][34] and the references therein), which cannot be directly solved by Equation (4), but behind their solvability is hidden the equation.…”

confidence: 99%

“…A related solvable system of difference equations was treated in [12]. Since that time various modifications of the method have been often used (see [13,14] and the references therein for some related difference equations, as well as [15][16][17] and the references therein for some related systems of difference equations). It should be pointed out that the systems are usually symmetric or close-to-symmetric, whose study was popularized by Papaschinopoulos and Schinas ( [18][19][20][21][22][23][24]).…”

confidence: 99%