## anonymous 4 years ago 2013 + k is a perfect square . Find all the possible values of k.

1. Mr.Math

You want to find all values of k such that $$2013+k=n^2 \implies k=n^2-2013$$, which has infinitely many solutions over the integers. Thus there are infinitely many k such that $$2013+k$$ is a perfect square.

2. dumbcow

x^2 = 2013 + k -> k = x^2 -2013, for all integers x>0

3. anonymous

k>=-2013

4. anonymous

and the smallest k is =-2012

5. anonymous

k=-2013 is that possible?

6. anonymous

(a+b+c)^2 = (2013 + k) is the original equation.

7. anonymous

are we looking for solution in R or C?

8. anonymous

In integers.

9. anonymous

Mr. Math and dumbcow seem right..

10. anonymous

a,b,c are also integers?

11. anonymous

yes

12. EarthCitizen

there should be only two values of k ?

13. anonymous

no,you are supposed to find all the possible values .

14. anonymous

all possible values seem infinite..

15. anonymous

1 more condition : a^ + 2bc = 2012, b^2 + 2ca = 1,c^2 + 2ab = k.

16. anonymous

(:

17. Mr.Math

Lol, Could your write the whole problem so we can help?

18. anonymous

If a, b, c are integers such that a^ + 2bc = 2012, b^2 + 2ca = 1,c^2 + 2ab = k.Then,find all the possible values of k.

19. anonymous

$ac \le0 \qquad a \le0 \quad or \quad c \le0$

20. anonymous

is there any options?