Let's understand the factor method of Diophantine equations step-by-step. Aso, try the question related to it.
Diophantine Equations
Consider an equation for which we seek only integer solutions. There is no standard technique of solving such a problem, though there are some common heuristics that you may apply. A simple example is $ x^2 - y^2 = 31$. Suppose we wish to find out the integer solutions to this equation.
First notice that if 'x' and 'y' are solutions, so are '-x' and '-y' (and vice versa). So it is sufficient to investigate positive solutions.
The factor method relies on the following steps:
Illustration
$ x^2 - y^2 = 31 \newline (x-y)(x+y) = 31 $
But 31 is a prime. So the only way 31 can be written as a product of two positive numbers is 1 times 31.
Since x-y is smaller, the only possibility is x-y=1, x+y=31, giving solutions x=16, y=15
Problems
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
