If 200 is added to a positive integer I, the result is a square number

 If 200 is added to a positive integer I, the result is a square number

If 200 is added to a positive integer I, the result is a square number. If 276 is added to to the same integer I, another square number is obtained. Find I.

Answer：
I + 200 = A2 : 200 added to I (unknown integer) gives a square.
I + 276 = B2 : 276 added to I (unknown integer) gives another square.
B2 = A2 + 76 : eliminate I from the two equations.
add squares A2 (0, 1, 4, 9, 16, 25,...) to 76 till you obtain another square B2.
76 + 182 = 400 = 202
A2 = 182 and B2 = 202
I = A2 - 200 = 124