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.

 Jun 24, 2024

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 \(\boxed{x=1+2k,\space y=−2−5k}\)

 Jun 24, 2024

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