When given questions like "What is the last digit of the result to 3^56?", I usually look for a recurring pattern involving smaller powers of 3. In this question for example, the recurring pattern for the last digit is 3, 9, 7, 1, 3, 9, 7 , 1, 3, 9, ... I use a similar technique when faced with problems such as "What is the remainder when 2^2010 is divided by 7". However, my textbook presents the solution to these problems using modulos of which I am not familiar with and my textbook won't explain them very well. So, could you please introduce me to modulos as well as how they relate to such questions?
Additionally, it would be greatly appreciated if you also explained problems using modulos such as "Find the smallest number which when divided by 3 gives a remainder of of 1; when divided by 4 gives a remainder 2; when divided by 5 gives a remainder of 3; and when divided by 6 gives a remainder of 4.
For the above problem I usually just find the LCM of 3, 4, 5 and 6 which is 60 and then minus 2 = 58.
Thank you so much:)