Question

3power1989 is divided by 7 remainder is

Answer 1

HI MATE
HERE IS YOUR SOLUTION
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3 ^ 1989 = 3 ^ 3*663 = 27 ^ 663 = (21+6)^663

NOW WE WILL EXPAND THIS , ALL TERMS BUT THE LAST ONE WILL HAVE 21 AS MULTIPLE AND THUS WILL BE DIVISIBLE BY 7 . THE LAST TERM WILL BE 6^663 IS DIVIDED BY 7 .
6^1 DIVIDED BY 7 YIELDS REMAINDER OF 6 6^2 DIVIDED BY 7 YIELDS REMAINDER OF 1
6^3 DIVIDED BY 7 YIELDS REMAINDER OF 6

THE REMAINDER REPEATS IN BLOCK OF TWO : {6-1}{6-1}{6-1} ... WHEN THE POWER IS ODD REMAINDER IS 6 WHEN THE POWER IS EVEN REMAINDER IS 1
SO , THE REMAINDER WHEN 6^663 = 6^ odd .....
THEREFORE THE ANSWER IS 6
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