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- Feb 13, 2012

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The number 65537 is not a 'whatever prime', it is aCompute the least residue of 3^215 (mod 65537) (65537 is prime).

I've tried to use Euler's theorem, Fermat's little theorem and Wilson's theorem, but nothing seems to work, please help.

$\displaystyle 3^{\frac{F_{n}-1}{2}} = -1\ \text{mod}\ F_{n}\ (1)$

For n=4 the (1) becomes...

$\displaystyle 3^{2^{15}} = -1\ \text{mod}\ 65537\ (2)$

In your post is written $\displaystyle 3^{215}$ and not $\displaystyle 3^{2^{15}}$... the question is: are You sure to have written correctly?...

Kind regards

$\chi$ $\sigma$

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