9 citations · 11 across the 7 of their papers we have counts for
7 papers
Process of "Primoverization" of Numbers of the Form a^n-1
Vladimir Shevelev
We call an integer N>1 primover to base a if it either prime or overpseudoprime to base a. We prove, in particular, that every Fermat number is primover to base 2. We also indicate…
Estimates of Newman Sum over Numbers Multiple of a Fixed Integer
Vladimir Shevelev
We prove that the ratio of the Newman sum over numbers multiple of a fixed integer which is not multiple of 3 and the Newman sum over numbers multiple of a fixed integer divisible…
A Short Proof of a Known Relation for Consecutive Power Sums
Vladimir Shevelev
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
On Ramanujan Cubic Polynomials
Vladimir Shevelev
A polynomial x^3+px^2+qx+r with the condition pr^(1/3)+ 3r^(2/3)+q=0 we call a Ramanujan cubic polynomial (RCP). We study different interest properties of RCP, in particular, an im…
On Monotonic Strengthening of Newman-like Phenomenon on (2m+1)-multiples in Base 2m
Vladimir Shevelev
We obtain exact and asymptotic expressions for the excess of nonnegative (2m+1)-multiples less than (2m)^k with even digit sums in the base 2m.
On the Newman sum over multiples of a prime with a primitive or semiprimitive root 2
Vladimir Shevelev
We obtain a simple relations for the Newman sum over multiples of a prime with a primitive or semiprimitive root 2. We consider the case of p=17 as well.