Let us show several; including the part already well known variants of find uncountable set solutions of equation Axm - Byn = C for natural numbers A,B,C,x,y,m,n of specified values A, B, C, in contrast to the Pillai's conjecture, in which it is assumed that the set of solutions of equation  is finite, and proof of Fermat's Last Theorem.
The Bulletin of Society for Mathematical Services and Standards (Volume 8)
K. R. R. Gandhi et al., "Some Anti-Solutions of the Pillai's Conjecture and Proof of Fermat's Last Theorem", The Bulletin of Society for Mathematical Services and Standards, Vol. 8, pp. 26-34, 2013