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

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what is the reminder when 6^17+17^6 is divided by 7?

Asked In TCS aditya (11 years ago)

Solved Vikas Goyal Read Solution (8)

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PARAG KAMRA  (11 years ago)

1) 6^17 mod 7=(7-1)^17 mod 7
so 7^17 divide by 7 and remainder will 0,so we only take (-1)^17 mod 7=-1

2) 17^6 mod 7=(7*2+3)^6
so now (7*2)^17 divide by 7 and remainder will 0,so we only take (3)^6 mod 7=
729 mod 7=1
now add (1)+(2)
-1+1=0(ans)

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Vikas Goyal  (11 years ago)

Hi All,

First break the sum into two parts..
(i) 6^17 (ii) 17^6

sol-(i)- By remainder theorem there are always two remainders for any number, i.e. one is in negative and another is positive. In this case when we divide 6 by 7 we will get two remainders that is 6 and (-1). We can take any of these but for simplicity we will take (-1) is the remainder. Now (-1)^17 = -1.

sol-(ii)-- we have 17^6.. Now. 17^6 /7 = 3^6/7= (3^3)^2/7 = 27^2/7 = (-1)^2/7 = 1 is the remainder.

On adding case -(i) and (ii)... we will get final remainder = 0.

Thanks.

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Nidhi Patel  (11 years ago)

how did this came : 17^6 /7 = 3^6/7 ,, can you please explain ! @vikas goyal

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Ravi.Bhagya Sri  (11 years ago)

the units digit in 6^n is always 6 so the units digit in 6^17 is 6
the units digit in 17^1=7
17^2=9
17^3=3
17^4=1 and the cycle repeats
so the units digit in 17^6 =9
in order to get the remainder of 6^17+17^6 when divided by 7 we have to add the units digits of 6^17 and 17^6 i.e., 9+6=15. the units digit is 5 which is the remainder..
ans is 5..

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kalyan pannuru  (11 years ago)

answer is 0

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manish kumar rai  (11 years ago)

answer is 0

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ARSHDEEP SINGH  (11 years ago)

The answer is 0

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sandhya  (10 years ago)

the answer was '0'

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