The greatest positive integer $ \mathrm{k} $, for which $ 49^{\mathrm{k}}+1 $ is a factor of the sum $ 49^{125}+49^{124}+\ldots 49^{2}+49+1 $, is : [JEE Main 2020, 7 Jan (Shift 1)]

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The greatest positive integer \( \mathrm{k} \), for which \( 49^{\mathrm{k}}+1 \) is a factor of the sum \( 49^{125}+49^…

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