+0  
 
0
1
1
avatar+867 

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.

 Jul 7, 2024
 #1
avatar+1256 
+1

We need to solve the system of equations

\(N \equiv 2 \pmod{5}, \\ N \equiv 2 \pmod{7}\)

 

Well, let's analyze this equation. 

N leaves a remainder of 2 when divided by 5 and 7. 

This means that N is two greater than the LCM of 7 and 5. 

 

This is because since it leaves the same remainder for both numbers, then it must be the same number. 

Therefore it is the LCM we are looking for. 

We have

\(LCM[5, 7] = 35\)

 

Adding two, we have \(35+2 = 37\)

 

thus, our answer is 37. 

 

Thanks! :)

 Jul 7, 2024

7 Online Users

avatar
avatar
avatar
avatar
avatar