Question

There is a natural number which becomes equal to the square of a natural number when is added to it, and to the square of another natural number when is added to it. Find the number.

Hard

Solution

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From the question, we can write that
+ =
+ =

=> = 68
=>
Now solve the equation for and
We get and .  (here which is and which can be written as by ignoring the point )
hence this the required number.

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