MHB Is there a solution to $x^2+y^2=1992$ for positive integers $x$ and $y$?

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The equation $x^2 + y^2 = 1992$ is examined for positive integer solutions. Participants argue that there are no such solutions, referencing the properties of sums of squares. The discussion includes a link to a related question for further exploration. The consensus is that the equation does not yield positive integer pairs. Therefore, $x^2 + y^2 = 1992$ has no positive integer solutions.
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$x^2+y^2=1992---(A)$
pove $(A)$ has no positive integer solution
 
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Albert said:
$x^2+y^2=1992---(A)$
pove $(A)$ has no positive integer solution

repeat question http://mathhelpboards.com/challenge-questions-puzzles-28/prove-x-y-1992-no-solution-13109.html?highlight=1992
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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