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Number Theory Level pending

$\large 807_{k} - 807_{k-1} = G8_{807}$

Find the base $k$ which will make the statement above true.

Note: For numbers with a base $n>10$ , let us assign A, B, C... etc to denote the remaining digits.

1 solution

Efren Medallo
Jun 20, 2015

We must first convert these numbers into decimal format,

that is

$(8k^2 + 7 ) - (8(k-1)^2 +7 ) = 16(807) + 8$

this simplifies to

$16k - 8 = 12920$

or $k = 808$ .