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Get Answers to all your Questions
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
Answers (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
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