# Find all positive integers which leaves remainder $1$ when divided by $3$, $2$ when divided by $4$, and $8$ when divided by $10$ [closed]

I have tried finding the general form but it appears that there is no general form. I could try just brute forcing it but it just is impractical.

PS: please only use the following theorems:

• Division Algorithm
• Bezout's Theorem
• Euclidean Algorithm
• Euclid Lemma
• Fundamental Theorem of Arithmetic
• Welcome to Mathematics SE. Take a tour. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. Mar 19 at 14:57
• Hint: Think of $n+2$, when $n$ is such integer. Mar 19 at 15:11
• Same as here, except you have $\,x\equiv -2\pmod{m_i}$ for all $i\ \$ Mar 21 at 21:19