We observe structure in the sequences of quotients and remainders of theEuclidean algorithm with two families of inputs. Analyzing the remainders, weobtain new algorithms for computing modular inverses and representating primenumbers by the binary quadratic form $x^2 + 3xy + y^2$. The Euclidean algorithmis commenced with inputs from one of the families, and the first remainder lessthan a predetermined size produces the modular inverse or representation.
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机译:我们用两个输入族在欧几里德算法的商和余数序列中观察结构。分析其余部分,我们获得了用于计算模逆和以二进制二次形式$ x ^ 2 + 3xy + y ^ 2 $表示素数的新算法。欧几里得算法从一个族的输入开始,并且小于预定大小的第一余数产生模逆或表示。
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