As shown in class, the Euclidean algorithm can be used to find solutions to equations of the form

\[ax + by = c.\]

Use the Euclidean algorithm to find integers $x$ and $y$ such that $5x + 2y = 1,$ with the smallest possible positive value of $x$.

State your answer as a list with $x$ first and $y$ second, separated by a comma.

Note that while there are many pairs of integers $x$ and $y$ that satisfy this equation, there is only one pair that comes from using the Euclidean algorithm as described in class, and this pair solves the problem.

Stanry Jun 24, 2024

#1**0 **

The smallest possible positive integer value of x would be 1, since 5 + 2*-2 =1. The answer to part one of your question is \(\boxed{1,-2}\)

im pretty sure the euclidean algorithm gives infinite solutions. after i did the process x=1+2k, y=−2−5k. so you just plug in values of k to get solutions. Im not sure what the question is asking but im pretty sure it wants \(\boxed{x=1+2k,\space y=−2−5k}\).

shmewy Jun 24, 2024