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MATH / Let n=3¹⁷+3¹⁰. It is known that 11 divides into n+1. If n can be written in base 10 as ABCACCBAB, where A,B,C are distinct digits such that A and C are odd and B is not divisible b…

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problem

Let n=317+310n = 3^{17} + 3^{10}. It is known that 1111 divides into n+1n+1. If nn can be written in base 1010 as ABCACCBABABCACCBAB, where A,B,CA,B,C are distinct digits such that AA and CC are odd and BB is not divisible by 33, find 100A+10B+C100A + 10B + C.
Plain-text mathematical notation (without MathML)
Let n=3¹⁷+3¹⁰. It is known that 11 divides into n+1. If n can be written in base 10 as ABCACCBAB, where A,B,C are distinct digits such that A and C are odd and B is not divisible by 3, find 100A+10B+C.
Original LaTeX notation
Let $n = 3^{17} + 3^{10}$. It is known that $11$ divides into $n+1$. If $n$ can be written in base $10$ as $ABCACCBAB$, where $A,B,C$ are distinct digits such that $A$ and $C$ are odd and $B$ is not divisible by $3$, find $100A + 10B + C$.

level

Level 5

type

Number Theory

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Source and history

task_id
eab5c046-a5c2-5686-936f-eeb1db0380f6
task_key
number~5ftheory--test--eab5c046-a5c2-5686-936f-eeb1db0380f6
task_revision_id
1
config / split
number_theory / test

Official source

initial import