$$ 3f + 280y = 1 $$
euclidean algorithm
$$ 280 = 3\cdot 93 + 1 $$
$$ 3 = 1 \cdot 3 $$
Back sub
$$ 1 = 280 + 3(-93) $$
my question is why a negative sign for 93? since in the euclidean algorithm the 93 is a positive one.
$$ 3f + 280y = 1 $$
euclidean algorithm
$$ 280 = 3\cdot 93 + 1 $$
$$ 3 = 1 \cdot 3 $$
Back sub
$$ 1 = 280 + 3(-93) $$
my question is why a negative sign for 93? since in the euclidean algorithm the 93 is a positive one.
In the Euclidean Algorithm finding the solutions to $$3f+280y=1$$ is equivalent to finding the solutions to $$3a-280b=1$$ And it's not abnormal to have solutions that are negative since solutions to the gcd equation are not unique.
There's a negative sign because $1=280+3(93)$ is false.