Bikash Chakraborty

Further investigations on a question of Zhang and Lü

Abstract In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

Proof Without Words: The Sum of Squares

Here, we prove wordlessly the sum formula of 1k + 2k + . . . + nk, k ∈ {1, 2, 3}. 1. 1 + 2 + . . .+ n = n(n+1) 2 2010 Mathematics Subject Classification: Primary 00A05, Secondary 00A66. 1 ar X iv :2 01 2. 11 53 9v 1 [ m at h. H O ] 2 1 D ec 2 02 0 2 B. CHAKRABORTY 2. 1 + 2 + ...+ n = n(n+1)(2n+1) 6 The bibliographic data of the above visual proof is “B. Chakraborty, Proof without words: the sum of squares, Math. Intelligencer, 40 (2018), no. 2, pp. 20.” SUMS OF POWERS OF NATURAL NUMBERS 3 3. 1 + 2 + ...+ n = ( n(n+1) 2 )2 References [1] B. Chakraborty, Proof without words: the sum of squares, Math. Intelligencer, 40 (2018), no. 2, pp. 20. [2] J. Barry Love, Proof without Words: Cubes and Squares, Math. Mag., 50 (1977), no. 2, pp. 74. [3] I. Richards, Proof without Words: Sum of Integers, Math. Mag., 57 (1984), no. 2, pp. 104. [4] G. Schrage, Proof without Words, Math. Mag., 65 (1992), no. 3, pp. 185. Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, West Bengal 700 118, India. Email address: bikashchakraborty.math@yahoo.com, bikashchakrabortyy@gmail.com

On the Uniqueness of Power of a Meromorphic Function Sharing a set with its k-Th Derivative

In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing

On some sufficient conditions of strong uniqueness polynomials

Abstract In this paper we shall find some sufficient conditions for a uniqueness polynomial to be a strong uniqueness polynomial, as this type of problem was never investigated by researchers earlier. We also exhibit some examples to substantiate our theorems.

A new type of unique range set with deficient values

In the paper, we introduce a new type of unique range set for meromorphic function having deficient values which will improve all the previous result in this aspect.