Sugar - cuboid

Pablo received from his master a cuboid composed of identical sugar cubes with a count between 1000 and 2000. The Pejko eat sugar cubes in layers.
On the first day, eat one layer from the front. On the second day, one layer from the right, and on the third day, one layer above. However, those three layers were each the same number of cubes. Find out how many cubes had the original cuboid. Find all possibilities.

Correct answer:

V1 =  1320
V2 =  1716

Step-by-step explanation:

1320=111012  1110=10(121)=(111)(121)=110  1716=121113  1211=11(131)=(121)(131)=132
PHP program:

for($a=1; $a<1000; $a++)
{
    for($b=1; $b<1000; $b++)
    {
        for($c=1; $c<1000; $c++)
        {
            $V = $a*$b*$c;
            if($V > 2000 || $V<1000)
            {
                continue;
            }

            if($a*$b == ($c-1)*$b && ($c-1)*$b == ($a-1)*($c-1))
            {
                echo "$V = $a * $b * $c <br>";
            }
        }
    }
}




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