Latest TCS Aptitude Question SOLUTION: wht is reminder when 6^17+17^6 is devided by 7?

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(#M40010974) TCS question Keep an EYE

wht is reminder when 6^17+17^6 is devided by 7?

Asked In TCS Jaimini Suthar (11 years ago)

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Jekin   (11 years ago)

6^17 mod 7=(7-1)^17 mod 7
so 7^17 divide by 7, middle term 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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joy dey  (11 years ago)

(7-1)^17 + (7*2+3)^6
binomial theorem
-1+3^6=728
728%7=0

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nidhi yadav  (11 years ago)

remainder when 6^17=6
and when 17^6=1
so the reamainder will be (6+1)/7=0

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N.Dayanithi  (11 years ago)

Answer: 0

6^17 = 6^4 * 6^4 * 6^4 * 6^4 * 6
17^6 = 17^2 * 17^2 * 17^2

(6^4)/7 gives remainder 1
6/7 gives remainder 6
so 1*1*1*1*6 = 6 . this is the remainder part of 6^17.
like wise (17^2)/7 gives remainder 2.
so 2*2*2 = 8 . this is the remainder part of 17^6.
6^17 + 17^6 = 6 +8 = 14 . 14/7 gives remainder 0.

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