Math Forum :: View topic – min value

Let x and y be the lengths of AB and BD respectively.
Then, (1)
Let (2), where k is an integer.
sub. (2) into (1), .
When , or . Since x and y are positive, we take . Sub. into (1), we have , rejected.
When , . We take . Sub. it into (1), we get Hence, the minumum integer value of the sum of [AB]+[BD] is 2.

For integer solution of x and y, there are no solution since .