Find the smallest positive integer whose square consists of 5 identical leading digits.
As an explicit example, would be the answer for 3 identical leading digits.
You have to place dots along a strip such that:
What is the maximum number of dots you can place on the strip?
Let be a function defined along the rational numbers such that for all relatively prime positive integers and . The product of all rational numbers such that can be written in the form for positive relatively prime integers and . Find .
Let be the smallest of the fractions that are greater than where are positive integers.
What is the value of ?
Let represent the repeating decimal for . The product can be expressed as where are positive integers and is as small as possible. can be expressed as where are coprime integers. What is ?
Note: refers to the repeating decimal evalauted in base .