SOLUTION: If you add 100 to the number you get a perfect square. If you add 168 to that number you get another perfect square. What is that number?

Question 99580: If you add 100 to the number you get a perfect square.
If you add 168 to that number you get another perfect square.
What is that number?
Found 2 solutions by checkley71, scott8148:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
21+100=121=11^2
121+168=289=17^2
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
n=number ... n+100=a^2 ... n+268=b^2

b^2-a^2=168 ... (b-a)(b+a)=168

factors of 168 ... 1,168 ... 2,84 ... 3,56 ... 4,42 ... 6,28 ... 8,21 ... 12,14

sum of factors is 2b, so it must be even ... 4,42 gives b=23, a=19 ... 23^2-19^2=168

n+100=19^2 ... n=261
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