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Math Help - Last digit

  1. #1
    Senior Member pankaj's Avatar
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    Last digit

    Find the last digit of 73^{75^{64^{76}}}
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  2. #2
    Super Member malaygoel's Avatar
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    the last digit is 3.

    Explanation:
    Last digit in 64^{76} is 6.

    now, 75^n has last two digits 25 if n is even, and last two digits are 75 if n is odd.

    Hence, 75^{64^{76}} has last two digits 25.
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  3. #3
    Moo
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    And to conclude, you have to use the fact that 73^{\varphi(10)}=73^4 \equiv 1 (\bmod 10)
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