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Algebra

Blazing goIITian

 Joined: 25 Jul 2011 Post: 322
30 Mar 2012 09:28:01 IST
3 People liked this
8
449
Modular Algebra :)
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

prove that these equations have no solutions

$1)x^2 + y^2 + z^2 = 800000007$

$2)a^2 + b^2 =10511$

$3)x ^ 2 + 7*y ^ 2 = 3$

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
30 Mar 2012 10:43:38 IST
1 people liked this

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..

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
30 Mar 2012 10:47:31 IST
1 people liked this

the question should be that these don't have integral solutions...

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

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
30 Mar 2012 10:59:17 IST
1 people liked this

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.

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
30 Mar 2012 12:55:33 IST
0 people liked this

$Thnx man ! U r absolutely Right dude :)$

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
30 Mar 2012 18:57:55 IST
0 people liked this

like to kar de bhai!!

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
30 Mar 2012 18:59:46 IST
0 people liked this

hey pls tell me what is a=_ b(mod n) pls i dont even know what it represent

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
30 Mar 2012 19:06:46 IST
0 people liked this

$a\equiv b (modn)$

$This means that when a is divided by n,the remainder is b$

$For example:$

$28\equiv 0 (mod7)$

$And If u have any orher doubt,Im ready to answer,pls post it ! :)$

$Like ma answer if it was helpful dude !!!$

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
30 Mar 2012 19:12:38 IST
0 people liked this

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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