Let $a$ be an integer and $p$ a prime number that divides both $5a-1$ and $a-10$. Show that $p$ also divides $a-3$.
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Tags: number theory, Divisibility
Let $a$ be an integer and $p$ a prime number that divides both $5a-1$ and $a-10$. Show that $p$ also divides $a-3$.