## An extension of Kronecker's theorem |

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8inoe absolute value adjoint appropriate integers arbitrarily given bound of F(t Charles Hermite Denoting determinants of order different from zero equations equivalent exists a real expressed form f fundamental system funotion geometrical problem geometry of numbers given number greatest common divisor Hence Henoe independent relations integers h integral coefficients integral values Kronecker's Theorem lemma Let F(t linear independence linearly linearly independent manifolds matrix mean value modulo Multiplying n-s dimensions necessary oondition numerically less oan take oofactor oonneoted original system paragraph planes positive number positive quadratio form possibility of satisfying possible linear relation preassigned number Professor Bohr Professor Harald Bohr quadratic real number relations with integral right hand member satisfy the inequalities series of real set of integers shortest distance Sinoe solution Stanford University suoh Suppose system of inequalities transformed unimodular substitution upper bound vanish simultaneously variables whenoe whioh