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Albert1
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$x^2+y^2=1992---(A)$
pove $(A)$ has no positive integer solution
pove $(A)$ has no positive integer solution
Albert said:$x^2+y^2=1992---(A)$
pove $(A)$ has no positive integer solution
When a problem or equation is stated to have "no positive integer solution," it means that there are no whole number solutions that satisfy the given conditions. In other words, there are no integers (positive whole numbers) that can be substituted into the equation to make it true.
Specifying "positive integer" solutions is important because it narrows down the search for solutions and makes the problem more specific. Without this specification, there could be an infinite number of solutions, including negative integers and non-integer values, which can make the problem more complex.
Yes, an equation can have no positive integer solution but still have other solutions. For example, the equation x^2 + 1 = 0 has no positive integer solution, but it does have complex solutions. This is because not all equations and problems have easily identifiable solutions, and some may require the use of more advanced mathematical concepts.
Proving that a problem has no positive integer solution typically involves using logical reasoning and mathematical techniques. One approach is to assume that a positive integer solution exists and then show that it leads to a contradiction or inconsistency. Another approach is to use mathematical theorems or properties to show that a positive integer solution is impossible.
Yes, it is possible for a problem to have no positive integer solution but still have a real solution. Real numbers include both positive and negative integers, as well as fractions and irrational numbers. So, a problem may have no positive integer solution, but it could still have a real solution involving non-integer values.