D. R. Kaprekar

Kaprekar also described the harshad numbers which he named harshad, meaning "giving joy" (Sanskrit harsha, joy +da taddhita pratyaya, causative); these are defined by the property that they are divisible by the sum of their digits. Thus 12, which is divisible by 1 + 2 = 3, is a harshad number. These were later also called Niven numbers after 1977 lecture on these by the Canadian mathematician Ivan M. Niven. Numbers which are harshad in all bases (only 1, 2, 4, and 6) are called all-harshad numbers. Much work has been done on harshad numbers, and their distribution, frequency, etc. are a matter of considerable interest in number theory today.

Working largely alone, Kaprekar discovered a number of results in number theory and described various properties of numbers. In addition to the Kaprekar's constant and the Kaprekar numbers which were named after him, he also described self numbers or Devlali numbers, the harshad numbers and Demlo numbers. He also constructed certain types of magic squares related to the Copernicus magic square. Initially his ideas were not taken seriously by Indian mathematicians, and his results were published largely in low-level mathematics journals or privately published, but international fame arrived when Martin Gardner wrote about Kaprekar in his March 1975 column of Mathematical Games for Scientific American. Today his name is well-known and many other mathematicians have pursued the study of the properties he discovered.

In 1963, Kaprekar defined the property which has come to be known as self numbers, as the integers that cannot be generated by taking some other number and adding its own digits to it. For example, 21 is not a self number, since it can be generated from 15: 15 + 1 + 5 = 21. But 20 is a self number, since it cannot be generated from any other integer. He also gave a test for verifying this property in any number. These are sometimes referred to as Devlali numbers (after the town where he lived); though this appears to have been his preferred designation, the term "self number" is more widespread. Sometimes these are also designated Colombian numbers after a later designation.

In 1949, Kaprekar discovered an interesting property of the number 6174, which was subsequently named the Kaprekar constant. He showed that 6174 is reached in the end as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical. Thus, starting with 1234, we have:

He attended the University of Mumbai, receiving his bachelor's degree in 1929. Having never received any formal postgraduate training, for his entire career (1930–1962) he was a schoolteacher at the government junior school in Devlali Maharashtra, India. Cycling from place to place he also tutored private students with unconventional methods, cheerfully sitting by a river and "thinking of theorems". He published extensively, writing about such topics as recurring decimals, magic squares, and integers with special properties. He is also known as "Ganitanand".

Kaprekar received his secondary school education in Thane and studied at Cotton College in Guwahati. In 1927, he won the Wrangler R. P. Paranjpe Mathematical Prize for an original piece of work in mathematics.

Dattatreya Ramchandra Kaprekar (Marathi: दत्तात्रेय रामचंद्र कापरेकर; 17 January 1905 – 1986) was an Indian recreational mathematician who described several classes of natural numbers including the Kaprekar, harshad and self numbers and discovered the Kaprekar's constant, named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well known in recreational mathematics circles.