What is an Integral Solution in Equations?

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An integral solution in equations refers to a solution where all variables take integer values, meaning no decimals or fractions are involved. In the context of the equation X^2 + Y^2 = 2aXY, finding a positive integral solution requires determining the value of 'a' such that X and Y remain integers. The discussion emphasizes that integral solutions are strictly whole numbers, reinforcing the definition of what constitutes an integral solution. The clarity around this concept is crucial for solving equations that demand integer outputs. Understanding integral solutions is essential for various mathematical applications beyond calculus.
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I've seen the word used in a context that is not related to calculus, but I never understood what it meant. What does it mean if an equation has an integral solution?

Here is a context:If X^2 +Y^2 = 2aXY has a positive integral solution, find the value of a. What does it mean to have an integral solution?
 
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It means that the solution is an integer.
 
It means that all the variables involved have their roots in form of integers.
 
As stated above, I believe that the solution is an interger (i.e. you won't have decimal or fractions as an answer).
 
CallMeShady said:
As stated above, I believe that the solution is an interger (i.e. you won't have decimal or fractions as an answer).
That's integer, but you are otherwise correct.
 

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