Hoon Balakram

Balakram was born in Jalandhar, Punjab in 1876. He received his master's degree from Panjab University and later passed the Mathematical Tripos from the St John's College, Cambridge.^[1]

In 1899 he passed the Indian Civil Service examination. Among other posts in his career he was appointed a Bombay High Court judge in 1929, a month before his death.^[1] He also served as the president of Indian Mathematical Society from 1921 to 1926.^[2]

Balakram proved in 1929^[1] that the expression ${\displaystyle {(2n)! \over (n+1)!(n+1)!}}$is an integer for infinitely many values of ${\displaystyle n.}$ He further showed that the expression is an integer for only eight values of ${\displaystyle n\leq 100}$, namely, 5, 14, 27, 41, 44, 65, 76, and 90.