Some Results on Number Theory and Analysis

In this work, we obtain bounds for the sum of integer solutions quadratic polynomials two variables form where src=image/13423078_02.gif> is a given natural number that ends in one. This allows us to decide primality Also get some results on twin prime numbers. addition, use special linear functionals defined real Hilbert space dimension src=image/13423078_03.gif> , which relation obtained: src=image/13423078_04.gif>, src=image/13423078_05.gif> src=image/13423078_06.gif>. When src=image/13423078_07.gif> or src=image/13423078_08.gif>, manage address Fermat's Last Theorem and equation src=image/13423078_09.gif>, proving both equations do not have positive solutions. For src=image/13423078_10.gif>, Cauchy-Schwartz Young's inequality were proved an original way.