Athmaraman, R. (2004). The Wonder World of Kaprekar Numbers. Chennai (India): The Association of Mathematics Teachers of India. Kaprekar, D. R. (1974). "The...

example, in base 10, 45 is a 2-Kaprekar number, because 45² = 2025, and 20 + 25 = 45. The numbers are named after D. R. Kaprekar. Let n {\displaystyle n} be...

In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with...

The number 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: Take any...

These numbers were first described in 1949 by the Indian mathematician D. R. Kaprekar. Let n {\displaystyle n} be a natural number. We define the b {\displaystyle...

Gunjikar, K. R.; Kaprekar, D. R. (1939), "Theory of Demlo numbers" (PDF), Journal of the University of Bombay, VIII (3): 3–9 Kaprekar, D. R. (1938a), "On...

as n-harshad (or n-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit...

Rochester who works in Number Theory D. R. Kaprekar – Mathematician who worked on Number Theory. He is known for Kaprekar constant Narendra Karmarkar – Mathematician...

Edwin Hubble Josephson constant – Brian David Josephson Kaprekar's constant – D. R. Kaprekar Kerr constant – John Kerr Khinchin's constant – Aleksandr...

amateur mathematicians: List of recreational number theory topics Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles Archived 2013-08-01...

Science, 1300-1800. Ákos Császár discovers the Császár polyhedron. D. R. Kaprekar discovers the convergence property of the number 6174. The use of lithium...

politician and sports administrator D. R. Kaprekar (1905–1986) — mathematician, discovered Kaprekar's constant and the Kaprekar number Sonali Kulkarni (born...

Hungarian dermatologist – Kaposi's sarcoma D. R. Kaprekar, Indian mathematician – Kaprekar constant, Kaprekar number Jacobus Kapteyn, Dutch astronomer –...

the People's Republic of China. The Malta Labour Party is founded. D. R. Kaprekar discovers the convergence property of the number 6174. Slavery in Kuwait...

these cubes as nasik as a respect to the great Indian Mathematician D R Kaprekar who hails from Deolali in Nasik District in Maharashtra, India. In 1905...

Artillery (d. 1981) January 17 D. R. Kaprekar, Indian recreational mathematician (d. 1986) Saeb Salam, 4-time prime minister of Lebanon (d. 2000) Guillermo...

Senior Wrangler R. P. Paranjpye Others Eknath Ghate Bapudeva Sastri Damodar Dharmananda Kosambi Chandrashekhar Khare D. R. Kaprekar Dinesh Thakur Kapil...

of Jesuits. Born: D. R. Kaprekar, Indian recreational mathematician; in Dahanu, Bombay province, British India (d. 1986) "Kaprekar numbers", where the...

connected components. country calling code for Uzbekistan 999 = 33 × 37, Kaprekar number, Harshad number In some parts of the world, such as the UK and Commonwealth...

these numbers satisfy S d ( n , k ) = S ( n − d + 1 , k − d + 1 ) , n ≥ k ≥ d {\displaystyle S^{d}(n,k)=S(n-d+1,k-d+1),n\geq k\geq d} (hence the name "reduced")...

giving b r + r = b 1 {\displaystyle b^{r+r}=b^{1}} . Equating the exponents on both sides, we have r + r = 1 {\displaystyle r+r=1} . Therefore, r = 1 2 {\displaystyle...

generalization: F n 2 − F n + r F n − r = ( − 1 ) n − r F r 2 {\displaystyle {F_{n}}^{2}-F_{n+r}F_{n-r}=(-1)^{n-r}{F_{r}}^{2}} F m F n + 1 − F m + 1 F...

Boston: Allyn and Bacon, LCCN 68-15225 Pettofrezzo, Anthony J.; Byrkit, Donald R. (1970), Elements of Number Theory, Englewood Cliffs: Prentice Hall, LCCN 77-81766...

numbers q and r such that a = b q + r  and  r < b . {\displaystyle a=bq+r{\text{ and }}r<b.} The number q is called the quotient and r is called the remainder...

k > 1 we have d ( n ) n ε ≥ d ( k ) k ε {\displaystyle {\frac {d(n)}{n^{\varepsilon }}}\geq {\frac {d(k)}{k^{\varepsilon }}}} where d(n), the divisor...

+(a+dn-d)^{3}} is given by F ( d , a , n ) = ( n / 4 ) ( 2 a − d + d n ) ( 2 a 2 − 2 a d + 2 a d n − d 2 n + d 2 n 2 ) {\displaystyle F(d,a,n)=(n/4)(2a-d...

{n}}} or a d ⋅ 2 r ≡ − 1 ( mod n )  for some  0 ≤ r < s . {\displaystyle a^{d\cdot 2^{r}}\equiv -1{\pmod {n}}\quad {\mbox{ for some }}0\leq r<s.} (If a number...

1 − x ) x k d x = ( − 1 ) z Γ ( z + 1 ) ( k − 1 ) ! ∑ r = 1 k − 1 s ( k − 1 , r ) ∑ m = 0 r ( r m ) ( k − 2 ) r − m ζ ( z + 1 − m ) , ℜ ( z ) > k − 1...

the original (PDF) on 2016-05-09, retrieved 2009-03-02. Bloch, R. M.; Campbell, R. V. D.; Ellis, M. (1948), "The Logical Design of the Raytheon Computer"...

root Sum-product Coding-related Meertens Other Dudeney Factorion Kaprekar Kaprekar's constant Keith Lychrel Narcissistic Perfect digit-to-digit invariant...