On integers which are representable as sums of large squares

2014/08/06 by Alessio Moscariello, Moscariello, Alessio · 1 citation
Mathematics · #11D07 #11P05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D07 #msc:11P05

paper · pdf · doi:10.48550/arxiv.1408.1435

6 pages. To appear in International Journal of Number Theory

arxiv created 2015/04/11 · arxiv updated 2015/04/14

Abstract

We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set \n²,(n+1)²,… \ is asymptotically O(n²), verifying thus a conjecture of Dutch and Rickett. Furthermore we ask a question on the representation of integers as sum of four large squares.

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• The Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes

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