منابع مشابه
ON kTH-POWER NUMERICAL CENTRES
We call the integer N a kth-power numerical centre for n if 1 + 2 + · · · + N = N + (N + 1) + · · · + n. We prove, using the explicit lower bounds on linear forms in elliptic logarithms, that there are no nontrivial fifth-power numerical centres for any n, and demonstrate that there are only finitely many pairs (N, n) satisfying the above for any given k > 1. The problem of finding kth-power ce...
متن کاملkTH POWER RESIDUE CHAINS OF GLOBAL FIELDS
In 1974, Vegh proved that if k is a prime and m a positive integer, there is an m term permutation chain of kth power residue for infinitely many primes [E.Vegh, kth power residue chains, J.Number Theory, 9(1977), 179-181]. In fact, his proof showed that 1, 2, 22, ..., 2m−1 is an m term permutation chain of kth power residue for infinitely many primes. In this paper, we prove that for k being a...
متن کاملFrequencies of Successive Pairs of Prime Residues
We consider statistical properties of the sequence of ordered pairs obtained by taking the sequence of prime numbers and reducing modulo m. Using an inclusion/exclusion argument and a cut-off of an infinite product suggested by Pólya, we obtain a heuristic formula for the “probability” that a pair of consecutive prime numbers of size approximately x will be congruent to (a, a+d) modulo m. We de...
متن کاملRevisiting Prime Power RSA
Recently Sarkar (DCC 2014) has proposed a new attack on small decryption exponent when RSA Modulus is of the form N = pq for r ≥ 2. This variant is known as Prime Power RSA. The work of Sarkar improves the result of May (PKC 2004) when r ≤ 5. In this paper, we improve the existing results for r = 3, 4. We also study partial key exposure attack on Prime Power RSA. Our result improves the work of...
متن کاملDiffraction from visible lattice points and kth power free integers
We prove that the set of visible points of any lattice of dimension n ≥ 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation. Using similar methods we show the same result for the 1-dimensional set of kth-power-free integers with k ≥ 2. Of special interest is the fa...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/15011