Table of Contents
How many solutions does Diophantine equation have?
General Solution to Linear Diophantine Equations. In the example above, an initial solution was found to a linear Diophantine equation. This is just one solution of the equation, however. When integer solutions exist to an equation a x + b y = n , ax+by=n, ax+by=n, there exist infinitely many solutions.
What is integral solution of equation?
Note: An Integral solution is a solution such that all the unknown variables take only integer values. Given three integers a, b, c representing a linear equation of the form: ax + by = c. Determine if the equation has a solution such that x and y are both integral values.
Which equation is Diophantine?
Diophantine equation, equation involving only sums, products, and powers in which all the constants are integers and the only solutions of interest are integers. For example, 3x + 7y = 1 or x2 − y2 = z3, where x, y, and z are integers.
What is an integer solution?
An integer solution is a solution such that all the unknowns take integer values). Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.
How many positive integer solutions are there of equation 3x 4y 63?
Detailed Solution ∴ 2 possible solutions are there.
How many integer solutions of $x^2 + y^2 = K$?
Source: StackOverflow answer by Alexandre C. Again, the number of integer solutions of $x^2 + y^2 = k$is four times the number of prime divisors of $k$which are equal to $1 \\bmod 4$. Knowing this, writing a program which gives the number of solutions is easy: compute prime numbers up to $46341$once and for all.
What is the value of x2-y2 = 1?
There are no positive integer solutions to the diophantine equation x2- y2= 1. Proof. (Proof by Contradiction.) Assume to the contrary that there is a solution (x, y) where x and y are positive integers. If this is the case, we can factor the left side: x2- y2= (x-y)(x+y) = 1.
What is the total number of solutions for x = 100 – 3Y?
For x, to be integer (100 – 3y) must be an even number so that it becomes divisible by 2. Since 100 is even , 3y must be even number. y< 33 and y should be even. y= [0,2,4,…32] . Since 0 is not a positive number. Hence, it is excluded. Therefore, Total number of solutions is 16. Hope that helps. 🙂 , Works as a Student and a Quoran.
What is the value of Y in 2x + 3y = 100?
Here the equation is 2x + 3y = 100. So,the sum of two even numbers or two odd numbers is always an even number. In this case x can be both even as well as odd positive integers, but y can only be positive even integer. According to the question x and y can only be positive integers so, possible values of y can be- y = {2,4,…,32}.