Discrete Math Homework Question | Mod Explanation | Test Prep

Bashyboy
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Homework Statement


I attached the problem as file.


Homework Equations





The Attempt at a Solution


I honestly do not know how to solve this problem. I have a test tomorrow, and this is really the only question that I am having difficulty with. I don't really know what mod means, especially in this context. I have tried to read the textbook, but it being rather convoluted, and me being constrained on time, was really quite futile.
 

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Hi Bashyboy! :smile:

a = 4 (mod 13) means that if you divide a by 13, the remainder is 4

(of course, that's the same as saying a - 4 = 0 (mod 13), ie a - 4 is divisible exactly by 13 :wink:)

show us what you get for c = 9a (mod 13) :smile:
 
Bashyboy said:

Homework Statement


I attached the problem as file.

Homework Equations



The Attempt at a Solution


I honestly do not know how to solve this problem. I have a test tomorrow, and this is really the only question that I am having difficulty with. I don't really know what mod means, especially in this context. I have tried to read the textbook, but it being rather convoluted, and me being constrained on time, was really quite futile.
Here's the attachment:
attachment.php?attachmentid=51751&d=1349900977.jpg


"I don't really know what mod means ..." and you have a test on this stuff tomorrow?

WOW !
 
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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