Question

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:

• A. 32
• B. 60
• C. 65
• D. 63

Answer 1

Answer: (D)

$1+49+492+\dots +49^{12}$
$={\left(49\right)}^{126}-1=\left(49^{63}+1\right)\frac{\left(49^{63}-1\right)}{\left(48\right)}$
So greatest value of $k=63$