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Is there some formal proof of Legendre symbol's being multiplicative? It seems pretty intuitive but I can't think of a way to formally show it?

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    $\begingroup$ You have to show that if $a$ and $b$ are not a square then $ab$ is a square. Once you know $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic it becomes obvious. $\endgroup$ – reuns Oct 14 '16 at 5:20

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