Fermat's right triangle theorem states that if \( a \), \( b \), and \( c \) are the lengths of the sides of a right triangle, with \( c \) being the length of the hypotenuse, then the only integer solutions to the equation \( a^2 + b^2 = c^2 \) occur for certain sets of values for \( a \), \( b \), and \( c \).
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