Question 1204377
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It sounds like the equation is {{{244[n] = 1024[4]}}}, meaning we're looking for the base n that makes that equation true.


244 base n = 1022 base 4
2n^2 + 4n + 4 = 1*4^3 + 0*4^2 + 2*4^1 + 2*4^0
2n^2 + 4n + 4 = 74
2n^2 + 4n + 4-74 = 0
2n^2 + 4n - 70 = 0
2(n^2 + 2n - 35) = 0
2(n - 5)(n + 7) = 0
n-5 = 0 or n+7 = 0
n = 5 or n = -7


Ignore the negative solution. Base numbers must be positive integers.


Therefore,
244 base 5 = 1022 base 4
or we can write it like this
{{{244[5] = 1022[4]}}}


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As a check,
244 base 5 = 2*5^2 + 4*5^1 + 4*5^0 = 74 base 10
which matches with the conversion of 1022 base 4.


The answer is confirmed.
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