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Every prime larger than 3 is arithmetic mean of other two primes
prime distribution of primes arithmetic progression Goldbach conjecture
2011/9/21
In this paper a new stronger proposition has been advanced and shown, that is, every prime larger than 3 is arithmetic mean of other two primes, and other important propositions that there are infinit...
Abstract: For the positive integer $n$, let $f(n)$ denote the number of positive integer solutions $(n_1, n_2, n_3)$ of the Diophantine equation $$ {4\over n}={1\over n_1}+{1\over n_2}+{1\over n_3}. $...
An identity on the $2m$-th power mean value of the generalized Gauss sums
2m-th power mean exact calculating formula generalized quadratic Gauss sums Number Theory
2011/9/5
Abstract: In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. This sol...
A mean value formula for elliptic curves
elliptic curves Weierstrass ℘ -function point multiplication division polynomial
2011/8/24
Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its ...