Fermats little theorem question

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Repeated squaring

Hi
I have tasked with solving the following equation:
x^6 \ \equiv 24 \ \mathbf{mod} \ 68
I'm told now that I need to use a method called "Repeated squaring to solve the equation above".
Any hints/idears on how I do this will be appriciated very much !
/Bob
 
Last edited:
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Bob19 said:
Hi
I have tasked with solving the following equation:
x^6 \ \equiv 24 \ \mathbf{mod} \ 68
I'm told now that I need to use a method called "Repeated squaring to solve the equation above".
Any hints/idears on how I do this will be appriciated very much !
/Bob
This should help:

http://web.usna.navy.mil/~wdj/book/node27.html

Alex
 
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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