On power values of sum of divisors function in arithmetic progressions
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 335-340pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: Let and be any given integers. It has been proven that there exist infinitely many natural numbers m such that sum of divisors of m is a perfect kth power. We try to generalize this result when the values of m belong to any given infinite arithmetic progression . We prove if a is relatively prime to b and order of b modulo a is relatively prime to k then there exist infinitely many natural numbers n such that sum of divisors of is a perfect kth power. We also prove that, in general, either sum of divisors of is not a perfect kth power for any natural number n or sum of divisors of is a perfect kth power for infinitely many natural numbers n.| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1569 |
Let and be any given integers. It has been proven that there exist infinitely many natural numbers m such that sum of divisors of m is a perfect kth power. We try to generalize this result when the values of m belong to any given infinite arithmetic progression . We prove if a is relatively prime to b and order of b modulo a is relatively prime to k then there exist infinitely many natural numbers n such that sum of divisors of is a perfect kth power. We also prove that, in general, either sum of divisors of is not a perfect kth power for any natural number n or sum of divisors of is a perfect kth power for infinitely many natural numbers n.
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