Question

If m, n are natural then number of pairs (m, n) for which m^2 +n^2+ 2mn-2013m-2013n =0 is​

Answer 1

m^2+n^2+2mn-2013m-2013n=0
=>(m+n)^2=2013(m+n)
Either m+n=0 or m+n=2013
Since, m and n are natural numbers, therefore, m+n cannot be 0
Therefore, m+n=2013
There is 2012 pairs of (m,n) to satisfy the equation.
(Reason: (m,n)=(1,2012),(2,2011),…..,(2012,1) so there is 2012 pairs)
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