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math

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Find the smallest values for a and b so that 21 base a equals 25 base b.

  • math -

    21 using base a
    = 2a + 1
    25 using base b
    = 2b+5

    2a+1 = 2b+5
    2a = 2b+4
    a = b+2

    in any base system for numbers, the base > 1
    so the smallest value of b = 2
    then a = 4

    The smallest values are a=4, b=2

    check:
    21 base 4 = 2(4)+1 = 9
    25 base 2 = 2(2) + 5 = 9

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