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lttlbbygurl
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I came across this Proposition in my book, and I know it's something really simple that I'm missing, but I can't seem to prove it.
Let n be an odd composite integer.
a) n is a pseudoprime to the base b where gcd (b,n)=1 if and only if the order of b in (Z/nZ)* divides (n-1).
b) If n is a pseudoprime to bases [tex]b_1[/tex] and [tex] b_2[/tex] then n is pseudoprime to base [tex]b_1b_2[/tex] and also to the base [tex]b_1b_2^{-1}[/tex]
Let n be an odd composite integer.
a) n is a pseudoprime to the base b where gcd (b,n)=1 if and only if the order of b in (Z/nZ)* divides (n-1).
b) If n is a pseudoprime to bases [tex]b_1[/tex] and [tex] b_2[/tex] then n is pseudoprime to base [tex]b_1b_2[/tex] and also to the base [tex]b_1b_2^{-1}[/tex]