Algebra

sathyaram's Avatar
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30 Mar 2012 09:28:01 IST
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Modular Algebra :)
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

prove that these equations have no solutions 

 

 



Comments (8)

hemang's Avatar

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30 Mar 2012 10:43:38 IST
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800000007 is 7(mod 8).

x^2, y^2 and z^2 can be 0,1,4(mod 8).

we can never get 7(mod 8) from them. :)

10511 is 3(mod 4).

a^2 and b^2 can be 0,1(mod 4).

again we can't get that..

 

 

 

 

 

hemang's Avatar

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30 Mar 2012 10:47:31 IST
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the question should be that these don't have integral solutions...

last one has a solution, y = 0. x = root3.

 

hemang's Avatar

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30 Mar 2012 10:59:17 IST
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i should have written.

y = 0, x = + , - root3.

x^2 + 7y^2 > 3. for all x , y = integers, and both x and y not simultaneously 0.

and if y = 0, x not equal to + 1 , - 1.

we can check these cases by hand.

 

 

 

 

sathyaram's Avatar

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30 Mar 2012 12:55:33 IST
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hemang's Avatar

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30 Mar 2012 18:57:55 IST
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like to kar de bhai!!

 


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30 Mar 2012 18:59:46 IST
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hey pls tell me what is a=_ b(mod n) pls i dont even know what it represent
sathyaram's Avatar

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30 Mar 2012 19:06:46 IST
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Blazing goIITian

Joined: 21 Mar 2012
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30 Mar 2012 19:12:38 IST
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noo bcoz u said yesterday that if u like my post i will like urs now i am saying the same




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