Latest self Aptitude Question SOLUTION: what remainder comes (6)^17+(17)^6 is divisible by 7

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what remainder comes (6)^17+(17)^6 is divisible by 7

raushan (12 years ago)

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Sanjana Patnaik  (12 years ago)

(6^17+17^6)/7
={(-1^17)+(3^6)}/7
=(-1+729)/7
=728/7
Remainder is zero

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Apoorv Verma  (12 years ago)

(6)^17+(17)^6
=(7-1)^17+(14+3)^6
=17C0(7)^17 + 17C1(7)^16*(-1)^1 + 17C2(7)^15*(-1)^2 + .... + 17C17(-1)^17
+ 6C0(14)^6 + 6C1(14)^5*(3)^1 + .... + 6C6(3)^6
Now all the terms except 17C17(-1)^17 and 6C6(3)^6 are divisible by 6
So reminder will be same as when sum of 17C17(-1)^17 = -17 and 6C6(3)^6 = 729 is divided by 7
i.e., (729-17)/7 = 717/7
Reminder is 5

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