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$Old$ June 17th, 2008, 06:44 AM

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$Default$ Primitive Elements

Good morning, one more question today:

w is a primitive element of Z_p (p prime)

for any a & b prove
w^a = w^b mod p iff a = b mod (p - 1)

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$Old$ June 17th, 2008, 09:41 AM

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Originally Posted by cryptocrow $View Post$

Good morning, one more question today:

w is a primitive element of Z_p (p prime)

for any a & b prove
w^a = w^b mod p iff a = b mod (p - 1)

If $w^a\equiv w^b \implies w^{a-b} \equiv 1$ since $w$ has order $p-1$ it means $p-1$ divides $a-b$ .

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$Old$ June 17th, 2008, 06:10 PM

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