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41 power^ 77 divided by seven the remainder is ? Ans 6

41 power^ 77 divided by seven the remainder is ? Ans 6

Grade:10

2 Answers

Rajat Pathak
40 Points
4 years ago
we can attempt it by using binomial theorem.  see how!!!
41=7*6+1
41^77=(7*6+1)^77
(7*6+1)^77=[77C0(7*6)^77]-[77C1(7*6)^76]+[77C2(7*6)^75]-.............+[77C76(7*6)]-[77C77*1]
HERE EVERY TERM IS DIVISIBLE EXCEPT THE LAST TERM WHICH IS -1.
THEREFORE THE REMAINDER IS-1.
WHICH CAN BE SAID AS 7-1=6
SO REMAINDER IS GONNA BE 6!!!
 
Rajat Pathak
40 Points
4 years ago
we can attempt it by using binomial theorem.  see how!!!
41=7*6+1
41^77=(7*6+1)^77
(7*6+1)^77=[77C0(7*6)^77]-[77C1(7*6)^76]+[77C2(7*6)^75]-.............+[77C76(7*6)]-[77C77*1]
HERE EVERY TERM IS DIVISIBLE EXCEPT THE LAST TERM WHICH IS -1.
THEREFORE THE REMAINDER IS-1.
WHICH CAN BE SAID AS 7-1=6
SO REMAINDER IS GONNA BE 6!!!!
 

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