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SECOND SOLUTIONS OF SOME WHOLE NUMBER EQUATIONS Smolygin V.D. Tel.: 8 916 834 87 96, E-mail: smolyg@yandex.ru The possibilities have been proved for the use of full-parallel solution method (FP method) for finding the second nontrivial solutions for some whole number equations. The second nontrivial solutions have been defined for the equation X2+Y2=Z2 and equation x2-Ay2=1 in whole numbers. For example, for the equation X2+Y2=Z2: - there are solutions: X1=m2-n2, Y1=2mn, Z1=m2-n2 [1]; - other solutions: X2=2n-m2-n2, Y2=22n-mn, Z2=2n-m2+n2 [2]. Here: m and n are mutually heterogeneous prime * numbers, m>n. The transformation of equations from multiple unknowns using FP method will define so many equations from one unknown as the number of unknowns contained in this equation; the highest degree of equation from one unknown is equal to the highest degree of monomials included into the equation from multiple unknowns. Two solutions are defined for the equation X+Y2=Z2 in whole numbers. Three solutions are defined for the equation X+Y3=Z3 in whole numbers. The second solution examples are given for some of the solved equations in square whole numbers and higher from multiple unknowns. * Two numbers one of which is even and another is odd are called heterogeneous. References. 1. G.Rademacher and O. Teplits Numbers and figures. Experiments of mathematic thinking. M.: State publishing house of physical-mathematical literature, 1962. 264 pages. 2. Smolygin V.D. Two roots of equation type X2+Y2=Z2 (Two solutions of the equation type X2+Y2=Z2) // United scientific journal 28. Moscow: Scientific publications' fund. 2005. pg. 68-76.