<s>[INST] Does the equation $a^2+d^2+4=b^2+c^2$ have any solutions? Does the equation have $a^2+d^2+4=b^2+c^2$ where $d<c<b<a$ have any integer solutions? This isn't a homework problem, but I need to know for a separate problem I'm doing. Wolfram Alpha isn't very helpful. 
 [/INST] Above equation shown below has parameterization:
$a^2+d^2+4=b^2+c^2$
$(2m)^2+(m-2)^2+(2)^2=(m+2)^2+(2m-2)^2$
For, $m=5$, we get:
$(10,3,2)^2=(7,8)^2$
Hence, the integer $4$ can be represented by sum difference of four squares.
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