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Math Help - Finding a unique cube root

  1. #1
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    Finding a unique cube root

    If we have an integer(say a) which ends in either 1,3,7 or 9 then how can one find another integer having at most the same number of digits as a but when cubed would end in exactly the same digit as a.
    E.g if a = 123
    then the required number is 927 because 123 ends in 3 and 927^3 also ends in 3 .
    Other examples:
    a = 435621 then required number is 786941
    Thanks.
    Last edited by pranay; April 19th 2011 at 11:18 PM.
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  2. #2
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    Hello, pranay!

    If we have an integer (say \,a) which ends in either 1, 3, 7 or 9,
    then how can one find another integer having at most the same number of digits as \,a
    but when cubed would end in exactly the same digit as \,a.

    E.g. .if a = 123, then the required number is 927
    because 123 ends in 3 and 923^3 also ends in 3.
    . . It could be any 3-digit number (or smaller) ending in 7.

    Another example: .a = 435621, then required number is 786941.
    . . It could be any 6-digit number (or smaller) ending in 1.

    Just make a list of the endings of cubes . . .

    . . a ends in: . . a^3 ends in:
    . . - - - - - - - - - - - - - - - - - -
    . . . . . 0. . . . . . . . . 0
    . . . . . 1. . . . . . . . . 1
    . . . . . 2. . . . . . . . . 8
    . . . . . 3. . . . . . . . . 7
    . . . . . 4. . . . . . . . . 4
    . . . . . 5. . . . . . . . . 5
    . . . . . 6. . . . . . . . . 6
    . . . . . 7. . . . . . . . . 3
    . . . . . 8. . . . . . . . . 2
    . . . . . 9. . . . . . . . . 9



    Example: .a = _ 4

    . . .Then: .b = _ 4


    Example: .a = _ _ 3

    . . .Then: .b = _ _ 7

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  3. #3
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    Thanks for that, but what if we need to find the smallest cube root which when cubed would end in the given number?
    like for the first example 927^3 would end in 123?
    Last edited by pranay; April 19th 2011 at 11:17 PM. Reason: modfiying the problem statement
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