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Diophantine equations (11D) - Diophantine m-tuples, i.e. sets with the property that the product of any two of its distinct elements is one less than a square; Simultaneous Pellian equations; Thue equations and inequalities

Elliptic curves (11G05) - Construction of high-rank elliptic curves; Integer points on families of elliptic curves

Diophantine approximations (11J) - Applications of Baker's theory and hypergeometric method; Continued fractions

Polynomials (11C08) - Indecomposability of polynomials and related Diophantine equations; Polynomial root separation

Fibonacci and Lucas numbers (11B39) - Diophantine and divisibility properties of binary recursive sequences; Connections with Diophantine m-tuples

Cryptography (94A60) - Elliptic Curve Cryptography; Cryptanalysis of RSA; Teaching

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