[数学] 求教

k>3的构造
m(m+k)=n(n+1) => 2m(2m+k)=2n(2n+2)
=>(2m+k)^2-k^2=(2n+1)^2-1 =>(2m+k)^2-(2n+1)^2=k^2-1
当k=2t(t>1)时 由于(2t^2)^2-(2t^2-1)^2=4t^2-1=k^2-1
此时2m+k=2t^2 =>m=t^2-t  2n+1=2t^2-1 =>m=t^2-1

当k=2t+1(t>1)时 由于(t^2+t+1)^2-(t^2+t-1)^2=4t^2+4t=k^2-1
此时2m+k=t^2+t+1 =>m=(t^2-t)/2  2n+1=t^2+t-1 =>n=(t^2+t)/2-1.