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(4^61 + 4^62 + 4^63 + 4^64 ) is divisible by [ ] 1) 3 2) 11 3) 13 4) 17 Note: Please help me solve this question by using Fermat’s theorem

(4^61 + 4^62 + 4^63 + 4^64 ) is divisible by [ ]

1) 3
2) 11
3) 13
4) 17
 
Note: Please help me solve this question by using Fermat’s theorem

Grade:7

4 Answers

Rahul Sanapala
44 Points
2 years ago
I think the answer to the above question is 10
(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85. = 460 x (4 x 85). = (460 x 340), which is divisible by 10
 
But the problem is, 10 is not given in the options..so kindly help.
Vikas TU
14149 Points
2 years ago
Dear student 
Please refer the below link , If you have any doubt , you can ask again . 
Good Luck 
Rahul Sanapala
44 Points
2 years ago
Yes, i refered to the link but the answer in there is 10, but 10 is not given in the options of my question. Do you know if we can solve this using Fermat’s little theorem. 
Yash Chourasiya
askIITians Faculty 256 Points
2 years ago
Dear Student

Given
461 + 462 + 463 + 464
→ 461 (1 + 4 + 42 + 43)
→ 461. (1 + 4 + 16 + 64)
→ 461. (85)
→ 461. (17*5)

So divisible by 17.

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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