Simple question, I’ve the following equation :

Solve[((25)^2 + x 260digitsConstant)/(y 67) == 300digitsConstant, {x, y}, Integers]

which can be solved by wolfram in this case, but I want $y×67$ to be a perfect square, so I tried :

Solve[((25)^2 + x 260digitsConstant)/((y 67 67)^2) == 300digitsConstant, {x, y}, Integers]

which that time hang because of the size of the constants. Is there an other way to rewrite the equation so that Mathematica can both solve it and have a resulting y which is a perfect square ?

Any constant large enough triggers the hang that prevents equation solving to finish : for example try,

260digitsConstant=0xdc4e445b69fe9483216d0fa85492b4656287bfb2fb4da5b65f0b86cc2c073f3ee24a038d3d0e88c78b722b466c5ca1c89792c368ed182a5a13df919cac7fe335173cd04f23769d5ef027290f34a86e8fcab014f1a19d395b0662c5c52424a38796dd6f2394047d716abb6f48cc46abee6e2be3168348b456d5878cbec0b57d0f
300digitsConstant=0xdc4e445b69fe9483216d0fa85492b4656287bfb2fb4da5b65f0b86cc2c073f3ee24a038d3d0e88c78b722b466c5ca1c89792c368ed182a5a13df919cac7fe3362dc72d3863d2ca8b36753d05dac4f1a77220ae2bbdbeb3e2b8e856a51da81c5f4295ea43a893923b7bc0cb9362f78c69a8e252d9af532e889ded7597a256f8e4