Latest TCS Aptitude Question SOLUTION: what is the remainder 6^17+17^6 is divided by 7?

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

Asked In TCS PRIYA NAMDEO (10 years ago)

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sireesha  (10 years ago)

17^6 can also be return like (7*2+3)^6 in this (7*2)^6 is divided by 7
so remaining 3^6/7 gives the reminder 1.....
In 6^17/7 there is a formula that
a^odd/a+1 gives remainder 6...
a^even/a+1 remainder 1....
from these reminder is 6.....
total remainder is 6+1=7
it is divided 7 gives remainder 0....

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ATIQUR RAHMAN  (10 years ago)

ans=0, as 6^17/7 rem 6 and 17^6 rem 1 so on adding 0 will be remainder

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swati kumari  (10 years ago)

ans=0
6^17/7=-1
17^6/7=1
1-1=0

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snehasis  (10 years ago)

remainder 0

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Abhishek Kumar  (10 years ago)

reminder=0

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naveen sharma  (10 years ago)

remainder 2

[6^17]/7 => [(36)^(17/2)]/7 => [(35+1)^(17/2)]/7 = remainder 1
[17^6]/7 => [(289)^3]/7 => [(287 =2)^3]/7 = remainder 1
adding both remainder we get 2

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Akanksha Mishra  (10 years ago)

its 1 as 6^17 gives rem 6
and 17^6 gives rem as 2
6+2=8/7=1

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satyam shivam  (10 years ago)

-1+1
so ans is 0.

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Suman Saurabh  (10 years ago)

(6^17 +17^6)/7=6/7+1/7=1
so remainder=0

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Guru Pranav  (10 years ago)

0

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saikat ghosh  (10 years ago)

we can solve it by concept of negetive remainder.
in 6^17/7 we can take its remaindr as -1. and in 17^6/7=> 3^6/7 gives the remainder 1.
so final ans is -1+1 = 0

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DIVYA KUKRETI  (10 years ago)

ans: 0
(7-1)^17/7+(7*2+3)^6/7
by negative remainder theorem:
-1^17/7+3^6/7
(6+1)/7
remainder=0

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