Let

(a) Decide whether .

(b) If find with

(c) If find with

Thank you all for checking this out, and any ideas/suggestions are very welcome. Thanks!

Printable View

- April 6th 2008, 09:36 PMProof_of_lifeSums of Squares problem.
Let

(a) Decide whether .

(b) If find with

(c) If find with

Thank you all for checking this out, and any ideas/suggestions are very welcome. Thanks! - April 6th 2008, 09:38 PMJhevon
- April 6th 2008, 10:04 PMProof_of_life
is the set of all sums of 2 squares.

Definition:

For each integer , greater than or equal to 1, let = { | = + . . . + for some ,..., },the set of all sums of squares.

Sorry, and thanks! - April 7th 2008, 12:33 AMOpalg
Hint (just to get you started): a square has to be congruent to 0 or 1 mod 4.

- April 7th 2008, 02:14 AMProof_of_life
So, let me say for the first one that n=17. Since 17 is congruent to 1 mod 4, that would satisfy part (a)? Since part (a) is satisfied, I would take part (b)'s approach and ignore part (c). The answer to part (b) would be , where a=4 and b=1.

I think I will get confused when n does not belong to , and I will not know how to approach part (c). - April 7th 2008, 02:22 AMProof_of_life
Sum of squares

I should have just googled this earlier! Thanks to the last replier, it got me on the right track.