## (x + y)(x + y + 1) = k*x*y

$(x + y) \,(x + y + 1) \; = \; k \, x \, y$

An interesting case of when    $k \; = \; 4$

$81\times 80 \; = \; 4\times 45\times 36 \; = \; 6480$
$289\times 288 \; = \; 4\times 153\times 136 \; = \; 83232$
$625\times 624 \; = \; 4\times 325\times 300 \; = \; 390000$
$1089\times 1088 \; = \; 4\times 561\times 528 \; = \; 1184832$
$1681\times 1680 \; = \; 4\times 861\times 820 \; = \; 2824080$
$2401\times 2400 \; = \; 4\times 1225\times 1176 \; = \; 5762400$
$3249\times 3248 \; = \; 4\times 1653\times 1596 \; = \; 10552752$
$4225\times 4224 \; = \; 4\times 2145\times 2080 \; = \; 17846400$
$5329\times 5328 \; = \; 4\times 2701\times 2628 \; = \; 28392912$
$6561\times 6560 \; = \; 4\times 3321\times 3240 \; = \; 43040160$
$7921\times 7920 \; = \; 4\times 4005\times 3916 \; = \; 62734320$
$9409\times 9408 \; = \; 4\times 4753\times 4656 \; = \; 88519872$
$11025\times 11024 \; = \; 4\times 5565\times 5460 \; = \; 121539600$
$12769\times 12768 \; = \; 4\times 6441\times 6328 \; = \; 163034592$
$14641\times 14640 \; = \; 4\times 7381\times 7260 \; = \; 214344240$

81,   289,   625,   1089,   …   are of the form   $(8 \, n + 1)^2$