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

Guest Apr 30, 2021

#1**+1 **

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

TaliaArticula Apr 30, 2021

#2**0 **

Nice job, TaliaArticula! Not so good at NT myself. Awesome and detailed solution!

MathProblemSolver101
Apr 30, 2021