| Popis: |
Sophie Germain contributed a great work in the field of number theory, theory of elasticity and in the proof of Fermat’s Last Theorem. While proving Fermat’s Last theorem, she had proved many results on prime numbers. Beyond prime numbers, she had proved many results in the field of number theory. Today, her proved results are known as Sophie Germain theorems, and classification of special form of prime numbers derived by her is called Sophie Germain prime numbers. Many people are still working in this area. Sophie Germain identity has been used currently to find some of the number forms which are factorizable. But, one can only check decomposability of the equation of form x ^ 4 + 4y ^ 4 using this identity. In the present art of work, an attempt is made to search out the generalized number form, so that one can find out which number forms are factorizable and which are not. It has also been shown that from the derived result, one can easily obtain the Sophie Germain identity as a special case. |
