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PowerMod[a, 1/r, m] fails to compute certain solutions.

Andrew Wang
Posted 11 years ago
The specific case that I found is:
PowerMod[411728896, 1/411728896, 10^9]

which returns:
PowerMod::root: The equation x^411728896 = 411728896 (mod 1000000000) has no integer solutions. >>

However, a solution is x=4.
POSTED BY: Andrew Wang
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Not sure how I missed this. Yes, this is a bug. Will get looked at.
POSTED BY: Daniel Lichtblau
Solve[ x^411728896 ==  411728896, x, Integers, Modulus -> 10^9]
Solve::mdom: Warning: Mathematica is ignoring domain specification Integers; option setting Modulus -> 1000000000 implies domain integers modulo 1000000000. >>

Roots::lrgexp: Exponent is out of bounds for function Roots. >>

Solve::munsp: Solve was unable to solve the system. Increasing the value of "MaxModularPoints" in SystemOptions["ReduceOptions"] may help. >>
POSTED BY: Frank Kampas
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