An Untold Algorithm: Summed Split Square Numbers

It’s time to uncover an undiscovered aspect of Algebra.

This book will introduce the world to an entirely new concept and theorem on a special type of numbers. We have all studied in our Mathematics classes about odd numbers, even numbers, prime numbers, composite numbers, perfect numbers and such, but never thought the following type of numbers would exist. Named Summed Split Square Numbers or SSS Numbers, this concept talks about when any number, once squared and then split into two equal halves, and after adding, will give you that original number.

Sounds difficult? For example, take the number 45. The square of 45 is 2025. After splitting it, we get 20 and 25, adding which we get the original number, 45.

Do we know how many such numbers exist in the universe? The answer is, infinite. Another interesting fact about SSS Numbers is that these exist in pairs, which makes them different from other type of numbers.

Again, for example, the number 45 has a pair, 55, which is also a SSS Number. The sum of these pairs is usually a multiple of ten. (45+55=100, which is a multiple of ten.) You will be surprised to know that last half of both the squares are the same; and in this case, it is 25.

Do we know why? The mystery will be resolved in this book where such fascinating facts and numbers are being dealt with, including the author’s derivation of the formulae as well as some work on a method introduced in this book to describe the numbers with repeated digits, which may open new horizons.

PC Bakshi hails from a middle-class family. Being the second-born in a family greatly interested in numbers, he developed a lifelong love with Mathematics. After completing his post-graduation in engineering, he started his career with Coal India. Even at this time, he used to spend all his spare time, if he got any, to solve mathematical and logical puzzles published in a reputed newspaper's brain-storming column. He always had a desire to excel in numbers, and take the subject the numbers to a different dimension. After retirement, he decided to actively pursue his passion and this book is the result of two years of hard work and dedication to his first love, the discovery of "untold numbers" for this world.