anonymous
  • anonymous
2013 + k is a perfect square . Find all the possible values of k.
Mathematics
katieb
  • katieb
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Mr.Math
  • 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.
dumbcow
  • dumbcow
x^2 = 2013 + k -> k = x^2 -2013, for all integers x>0
anonymous
  • anonymous
k>=-2013

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anonymous
  • anonymous
and the smallest k is =-2012
anonymous
  • anonymous
k=-2013 is that possible?
anonymous
  • anonymous
(a+b+c)^2 = (2013 + k) is the original equation.
anonymous
  • anonymous
are we looking for solution in R or C?
anonymous
  • anonymous
In integers.
anonymous
  • anonymous
Mr. Math and dumbcow seem right..
anonymous
  • anonymous
a,b,c are also integers?
anonymous
  • anonymous
yes
EarthCitizen
  • EarthCitizen
there should be only two values of k ?
anonymous
  • anonymous
no,you are supposed to find all the possible values .
anonymous
  • anonymous
all possible values seem infinite..
anonymous
  • anonymous
1 more condition : a^ + 2bc = 2012, b^2 + 2ca = 1,c^2 + 2ab = k.
anonymous
  • anonymous
(:
Mr.Math
  • Mr.Math
Lol, Could your write the whole problem so we can help?
anonymous
  • 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.
anonymous
  • anonymous
\[ac \le0 \qquad a \le0 \quad or \quad c \le0\]
anonymous
  • anonymous
is there any options?

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