# Find the greatest integer k for which 49^k +1 is a factor of the given sum 49^125 + 49^124 + ................ + 49^2 + 49 +1

Solution

⇒  1 + 49 + 49^2 + .................... + 49^125  = (49^126 - 1) / ( 49 - 1)

⇒   ( 49^63 +1) (49^63 -1) /48

⇒ ( 49^63 +1 )( (1 + 48)^63 ) - 1) /48

⇒ (49^63 +1) ( 1+ 48 I - 1)    ,Where is an integer

= (49^63 + 1) I

Greatest positive integer is k = 63

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-