On a conjecture about repdigits in k-generalized Fibonacci sequences

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On The Diophantine equation Fn+Fm=2a (2016, methodology): “To conclude this section of auxiliary results, we present the following lemma from [3], which is an immediate variation of the result due to Dujella and Pethő from [7], and will be one of the key tools used in this paper to reduce the upper bounds on the variables of the equation (1).”
k-generalized Fibonacci numbers which are concatenations of two repdigits (2021, unknown): “Diophantine equations involving repdigits were considered in several recent papers in which their authors found all repdigits that are perfect powers, or Fibonacci numbers, or generalized Fibonacci numbers, and so on (see [2, 5, 8, 15, 16, 17, 18, 20] for a sample of such results).”
Powers of two as sums of two k-Fibonacci numbers (2014, methodology): “This conjecture was confirmed shortly afterwards by Bravo and Luca [4].”