When is the sum of two squares a cube?

$2^2 \; + \; 2^2 \; = \; 2^3$

$2^2 \; + \; 11^2 \; = \; 5^3$

$18^2 \; + \; 26^2 \; = \; 10^3$

$52^2 \; + \; 47^2 \; = \; 17^3$

$110^2 \; + \; 74^2 \; = \; 26^3$

$198^2 \; + \; 107^2 \; = \; 37^3$

$322^2 \; + \; 146^2 \; = \; 50^3$

$488^2 \; + \; 191^2 \; = \; 65^3$

$702^2 \; + \; 242^2 \; = \; 82^3$

$970^2 \; + \; 299^2 \; = \; 101^3$

$1298^2 \; + \; 362^2 \; = \; 122^3$

$1692^2 \; + \; 431^2 \; = \; 145^3$

$2158^2 \; + \; 506^2 \; = \; 170^3$

$2702^2 \; + \; 587^2 \; = \; 197^3$

$3330^2 \; + \; 674^2 \; = \; 226^3$

$4048^2 \; + \; 767^2 \; = \; 257^3$

$4862^2 \; + \; 866^2 \; = \; 290^3$

$5778^2 \; + \; 971^2 \; = \; 325^3$

$6802^2 \; + \; 1082^2 \; = \; 362^3$

$7940^2 \; + \; 1199^2 \; = \; 401^3$

$(a^2 + b^2)^2 \; = \; (a^2 - b^2)^2 \; + \; (2 \, a \, b)^2$

multiplying both sides by $(a^2 + b^2)$

$(a^2 + b^2)^3 \; = \; (a^3 - 3 \, a \, b^2)^2 \; + \; (3 \, a^2 \, b - b^3)^2$

	mcdonewt on For which real number x is tan…
	John McMahon on (x^2 – 1) (y^2 – 1…
	Paul on smallest integer whose first n…
	benvitalis on smallest integer whose first n…
	benvitalis on smallest integer whose first n…

About benvitalis