Last Digits - 1

Find the last 3 3 digits of 20 1 201 201^{201} .


The answer is 201.

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1 solution

Harsh Khatri
Feb 16, 2016

20 1 5 1 ( m o d 1000 ) 201^{5} \equiv 1 \pmod {1000}

201 20 1 200 201 ( 1 ) 40 201 ( m o d 1000 ) \displaystyle \Rightarrow 201\cdot 201^{200} \equiv 201\cdot (1)^{40} \equiv \boxed{201} \pmod {1000}

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