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Our professor is abusing us: He wants us to compute $\text{ord}_{52579}2\text{, ord}_{52579}3\text{, and ord}_{52579}1001.$ Recall that the least positive integer $x$ such that $a^x\equiv1\pmod{n}$ is denoted $\text{ord}_na$.

I have a feeling that I may need to use a computer, but I do not have such computing power currently at my disposal. :(

Does anyone know of an anlytical approach to this? Thanks!

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    @Robert Israel: I think you mean 52579.2012-03-07

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