Let(adsbygoogle = window.adsbygoogle || []).push({}); pbe an odd prime. Letf(a)be a function defined foraprime topsatisfying the following properties:

(i)f(a)only takes the values ±1.

(ii) Ifa=b(modp), thenf(a)=f(b).

(iii)f(ab)=f(a)f(b)for allaandb.

Show that eitherf(a)= 1 for allaor thatf(a)= ([itex]\frac{a}{b}[/itex])

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# For the following properties, show that either f(a) = 1 for all a, or f(a) = Legendre

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