what will be the reminder on dividing 37^52 by 17

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19 Mar 2012 divide what will be the reminder on dividing 37^52 by 17: OPtion
1) 5
2) 7
3) 11
4) 13
5) 15
6) 3
7) 9
8) 1
9) any even number; Correct Option: 4 Best Solution (4)

Tijo Jose 12 years AGO

37^52 % 17
= ((37%17) ^ 52) % 17
= 3^52 % 17
= (3^48)%17 * (3^4)%17
= ((3^16)%17)^3 * (3^4)%17
= 1^3 * (3^4)%17 {3^16)%17 = 1, by Fermat's Little Theorem}
= (3^4)%17
= 81 % 17
= 13

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Suresh Varma P 12 years AGO

37^52 % 17 = ((37^10%17)*(37^10%17)*(37^10%17)*(37^10%17)*(37^12%17))%17

37^10 % 17 = 8
37^12 % 17 = 4
37^52 % 17 = (8*8*8*8*4)%17 = 13
Ans: option 4

Like? Yes (2) | No (2)

Gunaseelan 12 years AGO

37^4n Mod 17=4
Thus 37^52 Mod 17=4

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Ashish Pandey 12 years AGO

37^52
=(34+3)*(34+3)*(34+3)*.......*(34+3) {52 times}
So, indivisible part by 17 remains
=3*3*3......*3 {52 times}
therefore, 3^52/17 remainder=13

Like? Yes (1) | No (2)

Dimple

India

Punjab

Time: 00:01:33

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what will be the reminder on dividing 37^52 by 17

M4maths Previous Puzzles

19 Mar 2012 divide