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The greatest positive integer k, for which $49^{k} + 1$ is a factor of the sum $49^{125} + 49^{124} + ...... + 49^{2} + 49 + 1,$ is

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Correct option is D

49125+49124+....+49+1=49126−148 =4963+14963−148 ⇒4963+1 is a factor of the the sum. ⇒k=63

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The greatest positive integer k, for which 49k+1 is a factor of the sum 49125+49124+......+492+49+1,is

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The greatest positive integer k, for which $49^{k} + 1$ is a factor of the sum $49^{125} + 49^{124} + ...... + 49^{2} + 49 + 1,$ is