Question 20
Julia is training for the math Olympics. One day she decides to divide $2014$ by each of the positive integer divisors of $2015$. For each division, she writes the quotient in her notebook and the rest on a board.
a. Let's help Julia. Write the eight positive integer divisors of $2015$.
b. For each of the divisors, make the division and write a list with the quotients and another with the remains obtained.
c. At the end, Julia noticed a great "coincidence": the numbers written in the notebook were the same that were on the board, just written in a different order. Would it be a coincidence? Show that for any number $n$ that Julia chooses, if she calculates the quotient and the rest of the $n-1$ division for each of the $n$ divisors the numbers in the notebook and on the board They will be exactly the same, being only possibly written in a different order.
a. Let's help Julia. Write the eight positive integer divisors of $2015$.
b. For each of the divisors, make the division and write a list with the quotients and another with the remains obtained.
c. At the end, Julia noticed a great "coincidence": the numbers written in the notebook were the same that were on the board, just written in a different order. Would it be a coincidence? Show that for any number $n$ that Julia chooses, if she calculates the quotient and the rest of the $n-1$ division for each of the $n$ divisors the numbers in the notebook and on the board They will be exactly the same, being only possibly written in a different order.