Page 907. He’d never noticed it before — a thin, almost transparent sheet stuck between the final index and the back cover. On it, in handwriting so small it seemed whispered, was a single equation:
They found Professor Roy the next morning, asleep at his desk, head resting on page 907. The equation was solved. But in the margin, he had written a new one — unsolvable by radicals — and next to it: “The Eighth Gate. Seek page 1024.”
No one has found page 1024. Yet.
Anjan realized: this was Mapa’s secret — not just a textbook, but a map. Classical algebra wasn’t dead. It was a living labyrinth, and page 907 was the key.
[ x^5 + 10x^3 + 20x - 4 = 0 ]
Anjan chuckled. The Sapta-Dwara — the “Seven Gates” — was a legend among old Indian algebraists: seven impossible equations, each hiding a door to a lost mathematical truth. Most believed it was folklore. But here, in Mapa’s own copy? His hands trembled.
Gate 1: “Find all rational roots of (x^4 - 10x^2 + 1 = 0)” — easy, he smiled (Chapter 4, rational root theorem). Classical Algebra Sk Mapa Pdf 907
He worked through the night. The equation was quintic, yes, but cleverly constructed. Using Tschirnhaus transformations (Chapter 12, §4), he depressed it. Then he spotted it — a hidden quadratic in ((x + 1/x)) disguised by the coefficients. By dawn, he had reduced it to: