Integer Solutions to Stoichiometric Constraints in Reactions of α(2^a+2^b )(X^4+Y^4 )^2(6U^2+V^2 )=2^(l ) T^2 (C^2+D^2 )(Z^2-W^2 ) P^β wth α>0,β=1,2,3,4,5,6,7 , x<y<w

The provided abstract outlines an approach to model stoichiometric constraints in organic chemistry as Diophantine equations with over fourteen unknowns, using mathematical induction, trial-and-error, and Pythagorean triplets for integer solutions. Balancing organic reactions translates to linear Diophantine systems where unknowns are stoichiometric coefficients, ensuring atom conservation for elements like C, H, O, N. Molecular formula determination employs these equations to find integer atom counts matching mass or composition dataIn this paper, focused to find the general exponential integer solution of α(2^a+2^b )(X^4+Y^4 )^2 (6U^2+V^2 )=2^(l ) T^2 (C^2+D^2 )(Z^2-W^2 ) P^β With α>0, is derived from fixed value of β=1,2,3,4,5,6,7 and x