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Find the remainder when x= 5^5^5^5 (24 times 5) is divided by 24

Find the remainder when x= 5^5^5^5 (24 times 5) is divided by 24

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Harshit
 
23 times 5 is an odd natural number.
Hence
 
5^5^5^5.... = 23 times 5 = 2m +1
Now
24 times 5 = 5^(23 times 5) = 5^(2m+1) = 5* 5^(2m)
Hence 
 = 5* (5²)^m
 = 5(1+24)^m
 = 5(24k +1)
= 5* 24k + 5
Now when divided by 24
Remainder is 5
 
Regards
Arun (askIITians forum expert)
 

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