How to find all integers that when divided by 4 give a remainder of 3, when divided by 3 give a remainder of 2, and when divided by 2 give a remainder of 1?

Question

Mathematics

How to find all integers that when divided by 4 give a remainder of 3, when divided by 3 give a remainder of 2, and when divided by 2 give a remainder of 1? I was ill all week, I don’t understand anything in the textbook, tell me please.

Answer 1

Step 1) Go through mentally or on a piece of paper all the possible remainders from dividing by 12 and choose among them those that meet your conditions.
Step 2) Think of how to find all the numbers you need from the pattern found out.

Answer 2

=N*12-1
where N is a natural number
as a result we get: 11, 23, 35, 47, ...

Answer 3

When divided by 4, the remainder is 3; when divided by 3, the remainder is 2; when divided by 2, the remainder is 1.

The last condition is redundant, since it follows unambiguously from the first. If we discard it, we get the Chinese remainder theorem in its purest form.