The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Efficient Reduction of Polynomial Zero-One Optimization to the Quadratic Case
SIAM Journal on Optimization
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We investigate integer programs containing constraints of the type $\prod_{i\in I}x_i^{\alpha_i}=b$. Due to the number-theoretic nature of these constraints, standard methods based on linear algebra cannot be applied directly. Instead, we present a reformulation resulting in integer programs with linear constraints and polynomial objective functions, using prime decompositions of the right-hand sides $b$. Moreover, we show that minimizing a linear objective function with nonnegative coefficients over bivariate constraints is possible in polynomial time.