Let $a, b$ and $c$ be nonzero digits. Let $p$ be a prime number which divides the three digit numbers $\overline{abc}$ and $\overline{cba}.$ Show that $p$ divides at least one of the numbers $a+b+c, a-b+c$ and $a-c.$
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Tags: number theory proposed, number theory
Let $a, b$ and $c$ be nonzero digits. Let $p$ be a prime number which divides the three digit numbers $\overline{abc}$ and $\overline{cba}.$ Show that $p$ divides at least one of the numbers $a+b+c, a-b+c$ and $a-c.$