Indian Mathematical Problems and Data Science

Each person gives coins to 99 other people, so the total number of coins exchanged is 100 * 99 = 9900.

The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The 10th number in the sequence is 55.

Tithi, Nakshatra, and Yoga are components of the Panchanga system. Rahu is a planet in Vedic astrology, but it is not a component of the Panchanga system.

Brahmagupta, an Indian mathematician and astronomer, is credited with the formalization of the concept of zero in the 7th century AD.

The 5th row of Pascal's triangle is 1, 4, 6, 4, 1. The sum of these numbers is 1 + 4 + 6 + 4 + 1 = 16.

Ramanujan's prime number theorem, Ramanujan's theta function identity, and Ramanujan's modular equations are famous theorems attributed to Srinivasa Ramanujan. Ramanujan's conjecture is a statement about the distribution of prime numbers that was later proven by Harald Cramér.

Rao's U-statistic, Rao's score test, and Rao's likelihood ratio test are statistical techniques developed by C. R. Rao. Rao's F-test is a statistical test developed by R. A. Fisher.

Kaprekar's constant, Kaprekar's number, and Kaprekar's routine are mathematical problems attributed to D. R. Kaprekar. Kaprekar's conjecture is a statement about the distribution of prime numbers that was later proven to be false.

Shakuntala Devi holds the records for calculating the 23rd root of a 201-digit number in 25 seconds, multiplying two 13-digit numbers in 28 seconds, and calculating the square root of a 100-digit number in 18 seconds. She does not hold the record for extracting the 29th root of a 100-digit number in 50 seconds.

Paranjpe's theorem on amicable numbers, Paranjpe's theorem on perfect numbers, and Paranjpe's theorem on Mersenne primes are mathematical theorems attributed to R. P. Paranjpe. Paranjpe's conjecture is a statement about the distribution of prime numbers that is still unproven.

Bhargava's theorem on the average rank of elliptic curves, Bhargava's theorem on the distribution of quadratic forms, and Bhargava's theorem on the Ramanujan-Petersson conjecture are mathematical theorems attributed to Manjul Bhargava. Bhargava's theorem on the Birch and Swinnerton-Dyer conjecture is a statement about the Birch and Swinnerton-Dyer conjecture that is still unproven.

Ramanujan's prime number theorem, Ramanujan's theta function identity, and Ramanujan's modular equations are famous theorems attributed to Srinivasa Ramanujan. Ramanujan's conjecture is a statement about the distribution of prime numbers that was later proven by Harald Cramér.

Rao's U-statistic, Rao's score test, and Rao's likelihood ratio test are statistical techniques developed by C. R. Rao. Rao's F-test is a statistical test developed by R. A. Fisher.

Kaprekar's constant, Kaprekar's number, and Kaprekar's routine are mathematical problems attributed to D. R. Kaprekar. Kaprekar's conjecture is a statement about the distribution of prime numbers that was later proven to be false.

Shakuntala Devi holds the records for calculating the 23rd root of a 201-digit number in 25 seconds, multiplying two 13-digit numbers in 28 seconds, and calculating the square root of a 100-digit number in 18 seconds. She does not hold the record for extracting the 29th root of a 100-digit number in 50 seconds.