JEE Main 2017 Mathematics question
If is divided by , then the remainder is:
Answer: (3)
Solution
Reduce the base modulo first:
27 = 28 - 1 ≡ -1 ±od 7.
Therefore
≡ (- = -1 ±od 7,
since the exponent is odd. A remainder must lie in , so convert to its positive representative:
-1 ≡ 6 ±od 7.
The remainder is — option (3). Equivalently, expand binomially:
27^
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