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Omni-MATH / Four positive integers x,y,z and t satisfy the relations

Problem

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problem

Four positive integers x,y,zx,y,z and tt satisfy the relations xy−zt=x+y=z+t. xy - zt = x + y = z + t. Is it possible that both xyxy and ztzt are perfect squares?
Plain-text mathematical notation (without MathML)
Four positive integers x,y,z and t satisfy the relations
xy−zt=x+y=z+t.
Is it possible that both xy and zt are perfect squares?
Original LaTeX notation
Four positive integers $x,y,z$ and $t$ satisfy the relations
\[ xy - zt = x + y = z + t. \]
Is it possible that both $xy$ and $zt$ are perfect squares?

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Source and history

task_id
4d004681-d178-5e15-98d5-69757e228abf
task_key
test--4d004681-d178-5e15-98d5-69757e228abf
task_revision_id
1
config / split
/ test

Official source

initial import