Vandita Patel

activity

20152026

most citedPerfect powers that are sums of consecutive cubes

12 citations · 31 across the 12 of their papers we have counts for

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Showing 2016Show all

2 papers · 1 filter

math.NT2016

On powers that are sums of consecutive like powers

Vandita Patel, Samir Siksek

Let $k \geq 2$ be even, and let $r$ be a non-zero integer. We show that for almost all $d \geq 2$ (in the sense of natural density), the equation $$ x^k+(x+r)^k+\cdots+(x+(d-1)r)^k=y…

math.NT2016★ 12 cited

Perfect powers that are sums of consecutive cubes

Michael Bennett, Vandita Patel, Samir Siksek

Euler noted the relation $6^{3} = 3^{3} + 4^{3} + 5^{3}$ and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gen…