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      Question

      Find remainder when 7103 is divided by 240.

      A 55 Correct Answer Incorrect Answer
      B 45 Correct Answer Incorrect Answer
      C 75 Correct Answer Incorrect Answer
      D None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Ο†(240)=64 β†’ 7⁢⁴ ≑ 1 mod 240 103 = 64+39 β†’ remainder = 7³⁹ mod 240 Cycle of 7 mod 16 = 7, 1 β†’ mod16=7 mod15: 7⁴ ≑ 1 β†’ so mod15=7Β³ ≑13 Combine via CRT β†’ remainder 103.

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