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JEE Main202331 Jan 2023Morning ShiftMathematicsBinomial TheoremActual

The remainder on dividing 5 99 by 11 is _____ .

Correct answer

0

Step-by-step solution

Now to divide 5 99 by 11 we need to check the cyclicity of power of 5 when divided by 11 , So remainder when 5 1 11 → 5   as remainder Similarly, 5 2 11 = 25 11 → 3   as remainder 5 3 11 = 125 11 → 4   as remainder 5 4 11 = 625 11 → 9   as remainder And 5 5 11 = 3125 11 → 1   as remainder So, rewriting the expression we get, 5 5 19 × 5 4 Now when 5 5 19 × 5 4 11 → 1 × 5 4 11   Now again simplifying we get, 5 4

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