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Omni-MATH / Compute the sum of all two-digit positive integers x such that for all three-digit (base 10) positive integers …x, then the three-digit (base 10) number …x.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Compute the sum of all two-digit positive integers xx such that for all three-digit (base 10) positive integers \underline{a} \underline{b} \underline{c}, if \underline{a} \underline{b} \underline{c} is a multiple of xx, then the three-digit (base 10) number \underline{b} \underline{c} \underline{a} is also a multiple of xx.
Plain-text mathematical notation (without MathML)
Compute the sum of all two-digit positive integers x such that for all three-digit (base 10) positive integers \underline{a} \underline{b} \underline{c}, if \underline{a} \underline{b} \underline{c} is a multiple of x, then the three-digit (base 10) number \underline{b} \underline{c} \underline{a} is also a multiple of x.
Original LaTeX notation
Compute the sum of all two-digit positive integers $x$ such that for all three-digit (base 10) positive integers \underline{a} \underline{b} \underline{c}, if \underline{a} \underline{b} \underline{c} is a multiple of $x$, then the three-digit (base 10) number \underline{b} \underline{c} \underline{a} is also a multiple of $x$.

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Source and history

task_id
f3c16340-d3a1-56f3-8079-4463d090c79c
task_key
test--f3c16340-d3a1-56f3-8079-4463d090c79c
task_revision_id
1
config / split
/ test

Official source

initial import