Congruences:

Show by congruences that

q^2 + 3r^2 + 6s^3 – 9p^5 = 2

has no solutions in Z.

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- January 6th 2009, 12:32 AMmaths900Congruence question
Congruences:

Show by congruences that

q^2 + 3r^2 + 6s^3 – 9p^5 = 2

has no solutions in Z. - January 6th 2009, 01:11 AMIsomorphism
Did you try reading the equation modulo three?

- January 6th 2009, 04:45 AMmaths900
- January 6th 2009, 05:18 AMvincisonfire
In the equation becomes because 3,6 and 9 are in the equivalence class of 0.

What are the squares in ? - January 6th 2009, 07:44 AMmaths900
- January 6th 2009, 08:06 AMvincisonfire

- January 6th 2009, 08:29 AMmaths900
- January 6th 2009, 08:32 AMvincisonfire
No problem. We all have to start somewhere. It will seem simple to you in few weeks from now.

- January 6th 2009, 08:34 AMmaths900
- January 6th 2009, 09:01 AMmaths900
- January 6th 2009, 09:46 AMvincisonfire
Yes, because there is no elements in mod3 such that its square is 2.