Question

About an integer A, we know that
1. It has a remainder of 5 when being divided by 11,

2. A remainder of 4 when divided by 9

3. A remainder of 5 when divided by 7

4. A remainder of 4 when divided by 5

What is the remainder when A is divided by 3?

Answer 1

from 2 we know a=9q+4
so when divided by 3
we have
a=3(3q)+4=3(3q)+3+1=3(3q+1)+1=3q'+1
so theremainder when A is divided by 3 is 1

Answer 2

nice

Answer 3

thank you

Answer 4

How did I not think of that?