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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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algebraic number theory
cryptography
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gptkbp:defines
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polynomial equations with integer coefficients to be solved over the integers
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gptkbp:example
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gptkb:Fermat's_Last_Theorem
ax + by = c
x^2 + y^2 = z^2
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gptkbp:field
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number theory
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gptkbp:namedAfter
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gptkb:Diophantus_of_Alexandria
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gptkbp:notableAchievement
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Fermat's Last Theorem proved by Andrew Wiles
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gptkbp:property
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undecidable in general
finite or infinite number of solutions
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gptkbp:relatedTo
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gptkb:Pell's_equation
gptkb:Hilbert's_tenth_problem
linear Diophantine equation
quadratic Diophantine equation
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gptkbp:solvedBy
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integer solutions
natural number solutions
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gptkbp:studiedBy
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gptkb:mathematician
gptkb:ancient_Greece
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gptkbp:bfsParent
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gptkb:Euclidean_algorithm
gptkb:Fermat's_Last_Theorem
gptkb:Hardy–Littlewood_circle_method
gptkb:Number_theory
gptkb:Chinese_remainder_theorem
gptkb:Diophantine_approximation
gptkb:Frobenius_coin_problem
gptkb:Hasse_principle
gptkb:Louis_Mordell
gptkb:Unsolved_Problems_in_Number_Theory
gptkb:Waring's_problem
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Diophantine equations
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