Ramanujan–Nagell equation
The Ramanujan-Nagell equation is an important equation in number theory. It is expressed as 2ⁿ – 7 = x², where n and x are natural numbers (positive integers). Interestingly, only five values of n satisfy this equation, making it a rare and intriguing case in mathematical analysis.
| n | x |
|---|---|
| 3 | 1 |
| 4 | 3 |
| 5 | 5 |
| 7 | 11 |
| 15 | 181 |
Using the principle of solve et coagula, we can sequentially list the values of n as 345,715. Calculating the Frequency Root yields: 345 × 715 = 246,675, which reduces to 246 + 675 = 921. The number 921 factors as 3 × 307, revealing a connection to the number 37.
Similarly, listing the values of x sequentially results in 13,511,181. Calculating its Frequency Root: 13 × 511 × 181 = 1,202,383, which simplifies further to 1 + 202 + 383 = 586. This number decomposes into 216 + 370, where 216 represents the Frequency Root of 'Omega', (24th letter in the Greek alphabet) and the number 37 is embedded within.