Latest self Aptitude Question SOLUTION: what will be the remainder when 6^17+17^6 is divided by 7?

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what will be the remainder when 6^17+17^6 is divided by 7?

Ankesh Srivastava (11 years ago)

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Vikrant Varshney  (11 years ago)

{(7-1)^17 + (287+2)^3}%7
={(-1)^17 + 2^3}%7
=(-1+8)%7
=0
so remainder is 0

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Vikrant Varshney  (11 years ago)

hey this is the method to find remainder of these que.
we can write 6 as(7-1) so if we explain (7-1)^17 in nCr series then last term will be 17C17*(-1)^17=-1 and remains will be divided by 7 so remainder for this is -1 and similarly we can write 17^6=(17^2)^3=(289)^3=(287+2)^3 which will have last term as 3C3*2^3=8=7+1(since 287 is divisible by 7), so it gives remainder 1.
then final remainder is -1 + 1=0

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Amit kumar  (11 years ago)

6/7 remainder= -1
17/7 remainder= 3
=>6^17+17^6 is divided by 7
=>(-1)^17+3^6 is divided by 7
=>(-1+729)/7
=> 728/7 => quotient is 104 and remainder is 0.

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pragya lachhwani  (11 years ago)

plz explain clearly

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