My impression was that the OP's main challenge was the long division part, so I intentionally only demonstrated one example of division, not the whole Euclidean algorithm.

Jul 17, 2023 · Your question is about the number of steps in a subtractive Euclidean algorithm. The total number of subtractions is exactly equal to the sum of all the quotients when using the …

May 15, 2021 · abstract-algebra polynomials euclidean-algorithm euclidean-domain function-fields Share Cite edited May 15, 2021 at 12:04

Oct 5, 2019 · How can I prove this with an euclidean algorithm (do not use an extended euclidean algorithm, that was made very clear by my teacher) I cannot use gcd, I must use the euclidean …

Hint: It is enough to verify the assertion for a single step of the Euclidean algorithm, The rest follows by induction on the length $\lambda$. So do one step of the Euclidean algorithm, …

After using the Euclidean algorithm to find the greatest common divisor between $ a = r_ {-1} $ and $ b = r_0 $ (see figure) I'm trying to express in a general way the solution (x and y) of the …

Since $3|369$, the equation has integral solutions. Then we find a way of writing $3$ as a linear combination of $147$ and $258$, using the Euclidean algorithm computation above, and the …

Oct 6, 2015 · What bound does Theorem 4.2.3 give for the number of steps the Euclidean Algorithm will take when performed on $a$ and $b$? Theorem 4.2.3 states "for any pair of …

For questions about the uses of the Euclidean algorithm, Extended Euclidean algorithm, and related algorithms in integers, polynomials, or general Euclidean domains.

Mar 25, 2015 · Can someone give me an explanation targeted to a high school student as to why finding thegcd of two numbers is faster using the euclidean algorithm compared to using …