Find smallest natural numbers $x,y$ such that
$$ 49x = 125y.$$
Will this require some special modular arithmetic property or am I missing something?
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x=125n and y=49n for any integer n. – Alessio K Jan 24 '20 at 20:17
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@DietrichBurde 0 is not being considered a natural number here – Jan 24 '20 at 20:18
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If you must use modular arithmetic than $\, n\equiv 0\pmod{\!49\ \&\ 125}\iff n\equiv 0\pmod{\!45\cdot 125}\ $ by [CCRT](https://math.stackexchange.com/a/2006919/242) – Bill Dubuque Jan 24 '20 at 21:21
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Not at all: it only requires high school arithmetic. This common number is nothing else than the l.c.m. of $49$ and $125$. Now these numbers are coprime, so …
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