On the sum of two squares and at most two powers of 2

نویسندگان

  • David J. Platt
  • Timothy S. Trudgian
چکیده

We demonstrate that there are infinitely many integers that cannot be expressed as the sum of two squares of integers and up to two non-negative integer powers of 2.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

بررسی اثر متقابل ژنوتیپ × محیط و پایداری عملکر‌‌د برگ خشک ژنوتیپ‌های توتون ویرجینیا با استفاده از رگرسیون تای (Tai) وAMMI

To determine the yield stability and adaptability of the genotype of tobacco, 5 genotypes of flue-cured tobacco were evaluated in experiment using a randomized completely block design (RCBD) with three replications at two locations including Rasht and Tirtash tobacco Research Centers (IRAN), during the growing season of 2008-2010 (four environment). The interaction of genotype × environment in ...

متن کامل

An Incremental DC Algorithm for the Minimum Sum-of-Squares Clustering

Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.

متن کامل

Quarternions and the Four Square Theorem

The Four Square Theorem was proved by Lagrange in 1770: every positive integer is the sum of at most four squares of positive integers, i.e. n = A2 + B2 + C2 + D2, A, B, C, D ∈ Z An interesting proof is presented here based on Hurwitz integers, a subset of quarternions which act like integers in four dimensions and have the prime divisor property. It is analogous to Fermat’s Two Square Theorem,...

متن کامل

Analysis of genotype × environment interaction for seed yield of promising Kabuli type chickpea (Cicer arietinum L.) promising lines

One of the most complicated issues in plant breeding programs is genotype by environment interaction. To evaluate seed yield stability of 18 chickpea promising lines, a field experiment was conducted using randomized complete block design with four replications in two cropping seasons (2018-19 and 2019-2020) in four research stations (Maragheh, Kurdistan West Azerbaijan and Hamedan), Iran. Comb...

متن کامل

Sum-Rate Maximization Based on Power Constraints for Cooperative AF Relay Networks

In this paper, our objective is maximizing total sum-rate subject to power constraints on total relay transmit power or individual relay powers, for amplify-and-forward single-antenna relay-based wireless communication networks. We derive a closed-form solution for the total power constraint optimization problem and show that the individual relay power constraints optimization problem is a quad...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017