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anemone
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Find all values of $(a,\,b)$ where they are positive integers for which $\dfrac{a^2+b^2}{a-b}$ is an integer and divides 1995.
A positive integer is a whole number that is greater than zero and does not have any decimal or fractional parts. It can be represented as 1, 2, 3, 4, and so on.
The first step is to identify the equation and determine the unknown variable. Then, use algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable on one side of the equation. Finally, substitute positive integer values for the variable and solve for the other unknown values.
No, a positive integer solution must be a whole number that is greater than zero. Negative numbers are not considered to be positive integers.
Yes, there are limitations to solving for positive integer solutions. The equation must have only one variable and the operations used must be allowed for positive integers. Also, the equation must have a finite number of solutions.
Positive integer solutions are limited to whole numbers that are greater than zero, while real number solutions can include any number on the number line, including fractions and decimals. Additionally, real number solutions can be positive, negative, or zero, while positive integer solutions must be greater than zero.