\(a^2-b^2+a+b=b^2\)
\(\Rightarrow a^2-ab+ab-b^2+\left(a+b\right)=b^2\)
\(\Rightarrow a\left(a-b\right)+b\left(a-b\right)+\left(a+b\right)=b^2\)
\(\Rightarrow\left(a-b\right)\left(a+b\right)+\left(a+b\right)=b^2\)
\(\Rightarrow\left(a-b+1\right)\left(a+b\right)=b^2\)
Gọi \(d=ƯCLN\left(a-b+1,a+b\right)\)
\(\Rightarrow b^2=\left(a-b+1\right)\left(a+b\right)⋮d^2\)
\(\Rightarrow b⋮d\)
\(\Rightarrow a+1⋮d,a⋮d\)
\(\Rightarrow1⋮d\)
\(\Rightarrow d=1\)
\(\Rightarrow a-b+1,a+b\) nguyên tố cùng nhau
\(\Rightarrow a+b\) là số chính phương
