Calculating Remainders: Solution to (1*1!+2*2!+...+12*12!) / 13

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The discussion focuses on finding the remainder of the expression (1*1! + 2*2! + ... + 12*12!) when divided by 13. Participants emphasize the importance of showing a personal attempt at solving the problem, in line with forum guidelines. They suggest exploring the factorial notation and manipulating the expression using properties of factorials, such as (k+1)! = (k+1)k!. The conversation encourages users to think critically and independently about the problem. Ultimately, the goal is to arrive at the solution through a structured approach.
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Homework Statement


What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.

Homework Equations

The Attempt at a Solution

 
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Young wolf said:

Homework Statement


What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.

Homework Equations

The Attempt at a Solution

We cannot give the answer. We give hints, to solve the problem by yourself.
Read about the Forum rules:
https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686783/
"Show us that you've thought about the problem.
The forum rules require that you show an attempt at solving the problem on your own."

What does n! mean? Can you write the expression (1*1!+2*2!+...+12*12!) entirely with factorials?
Note that (k+1)! = (k+1)k!, determine (k+1)! - k!.
 
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