Base Arithmetic Number Theory

Question

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1

480

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+10

Find the largest possible positive integer $x_{10}$ less than $2021_{10}$ such that $d(x_{11})^2=4d(x_{13})$ .

Notation clarification: $x_{k}$ is $x$ in base $k$

$d(x_{k})$ is the sum of the digits of $x$ in base $k$

seratonin Mar 5, 2021

seratonin · Answer 1 · 2021-03-05T10:51:57

Note: This can easily be done with simple coding.