Math Problem Statement
In a school, there are 5000 lockers, all closed. There are also 5000 students. Student number one goes through the school and opens every locker because each locker number is divisible by one. Student number two goes through and closes every locker divisible by two. Student number three goes through and opens every locker divisible by three. Student number four goes through and closes every locker divisible by four. This pattern continues until student number 5000 goes through and opens every locker divisible by 5000. Which lockers are left open? Show all work and explain your reasoning.
Solution
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Math Problem Analysis
Mathematical Concepts
Number Theory
Divisors
Perfect Squares
Formulas
Divisors of a number
Perfect square property
Theorems
Numbers with odd divisors are perfect squares
Suitable Grade Level
Grades 9-12
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