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Omni-MATH / Find all triples (a,b,c) of integers that satisfy the equations

Problem

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problem

Find all triples (a,b,c)(a, b, c) of integers that satisfy the equations a+b=c a + b = c and a2+b3=c2a^2 + b^3 = c^2
Plain-text mathematical notation (without MathML)
Find all triples (a,b,c) of integers that satisfy the equations 

a+b=c and a²+b³=c²
Original LaTeX notation
Find all triples $(a, b, c)$ of integers that satisfy the equations 

$ a + b = c$ and $a^2 + b^3 = c^2$

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