A direct and completely elementary proof of Bernoulli's famous formula for the sum of consecutive kth powers is given.doi:10.2307/2689348Jeffrey Nunemacher and Robert M. YoungMathematics MagazineJ. Nunemacher and R.M. Young, On the sums of consecutive Kth powers, Math. Mag. 60 (1987), 237...
Focuses on Gauss sums and Heilbronn's sums. Emergence of Gauss sums into Waring's problem, and other additive problems involving kth powers; Improvement of the application of Stepanov's method to bound the number of solutions for differe... DR Heath-Brown,S Konyagin - 《Quarterly Journal o...
New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum Focuses on Gauss sums and Heilbronn's sums. Emergence of Gauss sums into Waring's problem, and other additive problems involving kth powers; Improvement of... DR Heath-Brown,S Konyagin - 《Quarterly Journa...
3153. 所有数对中数位不同之和 Sum of Digit Differences of All Pairs 力扣 LeetCode 题解 05:24 2766. 重新放置石块 Relocate Marbles 力扣 LeetCode 题解 03:16 3098. 求出所有子序列的能量和 Find the Sum of Subsequence Powers 力扣 LeetCode 题解 14:24 2101. 引爆最多的炸弹 Detonate the Max...
Prove that any natural number n in N can be written as a sum of one or more, distinct powers of 2 (note 1 is also a power of 2). Show that the sum of the first 2n natural numbers is n(2n+1). Given that the Fibonacci sequence is defined F(0)...
M.: On the representations of a number as the sum of four fifth powers, J. London Math. Soc., to appear. Wisdom, J. M.: On the representations of a number as the sum of four kth powers, submitted. About this Article Title On the Representations of a Number as the Sum of Three...
Integers represented as the sum of one prime, two squares of primes and powers of <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="/proc/2009-137-04/S0002-9939-08-09603-2/gif-title0/img1.gif" ALT="$ 2$">
State the generalization to kth powers, where k > 2. No proof is needed. Disprove the following statement. Use only the definitions: "For any integers b and n, if b is odd and n is even, then b^n is even." Using...
Sum of Powers of Natural Numbers: A Simple Approach by a Mechanical EngineerConvenient formulae for finding the sums of Kth power of first n natural numbers may be useful in some engineering applications. The formulae for k = 1, 2 and 3, are commonly found in the literature. In this ...
Paul J L.On the sums of the kth powers of the first n integers[J].Math Reviews,1972,43 (2):43-48.Paul, J. L. On the sum of the kth powers of the first n integers[J]. Amer. Math. Monthly.1971,78:271-272.Paul J L. On the sums of the kth powers of the first n ...