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Math Help - Let p be an odd prime...

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    Let p be an odd prime...

    Let p be an odd prime, and suppose a number b has order t>1 mod p. Prove that 1+b+b2++bt-1 is congruent to 0 mod p.
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    Quote Originally Posted by NikoBellic View Post
    Let p be an odd prime, and suppose a number b has order t>1 mod p. Prove that 1+b+b^2++b^{t-1} is congruent to 0 mod p.
    p \mid b^t - 1=(b-1)(1 + b + \cdots + b^{t-1}) but p \nmid b-1 because o(b)=t > 1. (do we really need p to be odd?)
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