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(#M40011605) TCS question Keep an EYE

remainder of (6^17+ 17^6)/7 ?
options-
1, 6, 0 ,3

Asked In TCS (11 years ago)

Unsolved Read Solution (3)

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arumoy  (11 years ago)

remainder when 6^17 + 17^6 is divided by 7
6^17mod7....>(7-1)^17mod7=(-1)^17(because 7^17 is divisible by 7 ,so we avoid it and only take (-1)^17 mod 7=-1 .........(1)
17^6....>(7*2+3)^6 mod7=(3)^6 mod 7....729 mod 7=1 .......(2)
so now remainder when 6^17 + 17^6 is divided by 7
now eq (1)+(2) mod 7
(6^17 + 17^6)mod 7=(-1+1) mod 7=0 mod 7=0
ans is 0.

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vivek tomar  (11 years ago)

6^17 its unit digit is 6 and 17^6 its unit digit is 9 .according to the cyclicity of 6 in1st part and 7 in 2nd part .
6+9/7=15/7=1 is the remainder

Is this solution Helpfull? Yes (4) | No (13)  

nitin dutta  (11 years ago)

32+16+8=56

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