The greatest positive integer k, for which 49k+1 is a factor of the sum 49125+49124+⋯+492+49+1, is
A
32
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B
60
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C
65
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D
63
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Solution
The correct option is D63 1+49+492+⋯+49125=49126−149−1=(4963+1)(4963−1)48=(4963+1)((1+48)63−1)48 =(4963+1)(1+48I−1)48 ; where I is an integer. =(4963+1)I
Greatest positive integer is k=63