awesome220 said:Can anyone help me with this?
If gcd(r,s)=1 then prove that gcd(r^2-s^2, r^2+s^2)=1 or 2.
i'm so confused.
GCD (Greatest Common Divisor) is the largest positive integer that divides two or more numbers without leaving any remainder.
There are several methods for calculating GCD, including using prime factorization, Euclid's algorithm, or using a GCD calculator. The most commonly used method is Euclid's algorithm, which involves finding the remainder of the larger number divided by the smaller number, and then repeating the process with the smaller number and the remainder until the remainder is equal to 0. The last non-zero remainder is the GCD.
GCD is an important concept in number theory and is commonly used in various mathematical calculations, including simplifying fractions, finding equivalent fractions, and reducing algebraic expressions. It is also used in cryptography and coding theory.
No, GCD is always a positive integer. This is because it represents the largest positive number that can divide two or more given numbers without leaving a remainder.
GCD is used in various real-life situations, such as simplifying recipes, dividing items into equal groups, and finding the lowest common denominator in fractions. It is also used in computer science, such as in the implementation of algorithms and data structures.