Find Me
If 200 is added to a positive integer , the result is a perfect square. If 276 is added to the same integer , another perfect square is obtained. Find .
The answer is 124.
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1 solution
200+I=k^2 for some integer k ----> I=k^2-200 276+I=p^2 for some integer p ----> I=p^2-276 equating, we get: k^2-200=p^2-276
p^2-k^2=76
try 38(2) (The other factors don't qualify. Try to prove this)
(p-k)(p+k)=2(38) p-k=2 p+k=38
p=20, k=18 Therefore, I=124