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# number theory

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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
+336
+1

Hey there, Guest!

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
+805
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Nice job, TaliaArticula! Not so good at NT myself. Awesome and detailed solution!

MathProblemSolver101  Apr 30, 2021