What will be the remainder when 6^17+17^6 is divided by 7?
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6^17 wil, have last digit as 6.
17^6 will have last digit as 3. [The series of 7 power is 9, 3, 1, 7] i.e. 6%4 = 2
Explanation of second line: 7 to the power 2, 3, 4, 5 have last digits as 9, 3, 1 and 7 respectively. This cycle repeats for the next numbers. Then we divide 6 by 4 and get the remainder as 2. so we select second value i.e. 3.
therefore 6^17+17^6 will have last digit as 9.
Thus 9 divided by 7 will have remainder as 2. [Ans]
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