Let form an increasing arithmetic progression (AP) which consists of only positive terms. Let the minimum value of be for real . Then find the sum of all possible values of the common difference of AP.
Notation: denotes the absolute value function.
What is the value of ?
For real , find the minimum value of the expression below.
Define a function as follows
where
For certain positive integers and for all , this function always returns the lowest of the values . For example
.
Let be integer digits of a digit integer . What is the value of ?
If the minimum value of the expression above is , and it occurs when , where and are each coprime pairs of positive integers, find .