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What is the smallest positive integer n such that the rightmost three digits of n^2 and (n+2)^2 are the same?

 Apr 30, 2021
 #1
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Hey there, Guest!

 

So, let's solve your problem:

 

Step 1: Simplify both sides of the equation.

\(n^2=n^2+4n+4\)

 

Step 2: Subtract n^2 from both sides.

\(n^2−n^2=n^2+4n+4−n^2\)

\(0=4n+4\)

 

Step 3: Flip the equation.

\(4n+4=0\)

 

Step 4: Subtract 4 from both sides.

\(4n+4−4=0−4\)

\(4n=−4\)

 

Step 5: Divide both sides by 4.

\(\frac{4n}{4}=\frac{-4}{4}\)

 

Therefore, n=-1.

 

Hope this helped! :)

( ゚д゚)つ Bye

 Apr 30, 2021
 #2
avatar+742 
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Nice job, TaliaArticula! Not so good at NT myself. Awesome and detailed solution!

MathProblemSolver101  Apr 30, 2021

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