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anonymous
 one year ago
Explain why this problem is in a number theory book? I feel like it should be in a Cal 3 book.
Prove that if (xₒ,yₒ) is a solution of the linear Diopahntine equation ax  by = 1, then the area of the triangle whose vertices are (0,0), (b,a) and (xₒ,yₒ) is 1/2?
This could easily be proven using cross product
anonymous
 one year ago
Explain why this problem is in a number theory book? I feel like it should be in a Cal 3 book. Prove that if (xₒ,yₒ) is a solution of the linear Diopahntine equation ax  by = 1, then the area of the triangle whose vertices are (0,0), (b,a) and (xₒ,yₒ) is 1/2? This could easily be proven using cross product

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UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0The Diophantine equation was in my number theory book as well. An equation which only integer solutions are allowed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0eh, probably because it mentions linear Diophantine equations?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And there is this problem too. A man pays $1.43 for some apples and pears. If pears cost 17 cents each, and apples, 15 cents each, how many of each did he buy? O.O what the heck? this is 5th grade problem!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0oh I had that problem too... hey are you reading Number Theory by George Andrews?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyways, this just follows from the determinant: $$\left\det\begin{bmatrix}b&x_0\\a&y_0\end{bmatrix}\right=\leftby_0ax_0\right=1$$ which is the area of the whose edges are given by \((b,a),(x_0,y_0)\), so the triangle is simply half that: \(1/2\)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0I've used that book last year in my Elementary Number Theory class XDDDDDDDDDDD!!!!!!!! Luckily I didn't have to do that problem, but I was stunned when I saw that.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0I've heard that it's the most popular book.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Mostly the authors choose trivial examples in the start because the focus is on succcessfully applying a particular method, not on getting a quick answer

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0the second question translates to solving linear diophantine eqn \[17a+15p = 143\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that problem is fine, it's a Diophantine equation, too: $$15a + 17p = 143\\ 15a=143\pmod{17}\implies 2a=10\pmod{17}\implies a=5\pmod{17}\\17p=143\pmod{15}\implies 2p=10\pmod{17}\implies p=5\pmod{15}$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops, the second line is broken

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$2p=8\pmod{15}\implies p=8\pmod{15}$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0O: I did the second problem by guess and check. Never mind about it being 5th a grade problem ^^

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need someone to confirm this problem. Hold on...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://openstudy.com/users/sourwing#/updates/55adfc7be4b045595079d70b
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