Grade 77 grade maths

(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

Rahul Sanapala

6 Years agoGrade 7

4 Answers

Rahul Sanapala

6 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

6 Years ago

Dear student

Please refer the below link , If you have any doubt , you can ask again .

https://www.askiitians.com/forums/Algebra/22/30987/math-problem-2.htm

Good Luck

Rahul Sanapala

6 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

6 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