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There is a generalization of the Legendre symbol for composite values of p, the Jacobi symbol, but its properties are not as simple: if m is composite and the Jacobi symbol then a N m, and if a R m then but if we do not know whether a R m or a N m. If m is prime, the Jacobi and Legendre symbols agree.
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Some Related Sentences
There and is
There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.
There is little time for the men in the command centers to reflect about the implications of these clocks.
There is a New South emerging, a South losing the folksy traditions of an agrarian society with the rapidity of an avalanche -- especially within recent decades.
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There and generalization
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There are reasons for believing that he was mistaken, and that the forms remain equivalent even under that extreme generalization of and ; but the point is this: it is not a question of conventional definition and formal truth ; it is a question of objective definition and real truth.
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There exists a slight generalization of Kummer theory which deals with abelian extensions with Galois group of exponent n, and an analogous statement is true in this context.
There is an opinion that an MIPT specialist / Master's diploma may be roughly equivalent to an American Ph. D. in physics — possibly an undue generalization which, however, may be true in some cases.
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There is no natural generalization to more than three players which divides the cake without extra cuts.
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