let F= { 0=a1, a2,a3,a4.....an} be a finite field. show that(adsbygoogle = window.adsbygoogle || []).push({});

(1+a2)(1+a3).........(1+an) = 0.

when n is odd, it's simple since 1 belongs to F. then odd number of elements are left( they're distinct from 0 and 1). at least one of them, say x,must have itself as its inverse. x^2 = 1 implies x=-1 ( since x != 1)...so the result is true.

for n even and the case where none of them are inverses of themselves, can somebody suggest a solution???

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# Finite fields

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