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Hi Johnathon bresly;
I have quite understand it,30 minutes ago I searched in wikihow and found a similar way.
Hi; To solve this you form the following table: The first two rows are just the GCD algorithm applied to 74 and 54. The last row is generated by the following trick. See the 1 and the 0 that are boxed off they are always given. To get the 2 you take the number before it (second boxed number (1)) and multiply it by the top row number that is in the same column. So that is (1)(2), now you add the number 2 before it ( second boxed number ) (1)(2) +1 = 3. To get the next number you take number before it and times it by the top row, same column and add the number before that. (2)(1)+1 = 3. Next is (3)(2)+2 = 8. Last is (8)(1)+3 = 11. Now the whole table is filled up and ready for the final stage. Cross multiply the first 2 numbers in the second and third row. So x =8 and y = 11 is a solution.
It will be better if you post it.
Hi;
I will try my best to understand those methods,so please post them.
Hi;
Oh,I understand it now,but what is it with the other solution method.
This back substitution is a little complex,is there any rule for which number to substitute in the steps?
Hi Johnathon bresly; First find the gcd(1124,84), which equals 4. Here are the steps. Now we back substitute starting with the second to last step. So then a solution of is x = 8 and y = 107 There is a much better way to do this using a backward recurrence but you would need to go to another page to see it.
I am sorry but i use mobile phone to go to internet and that link is not visible to me so it'd be better if you explain it here,and i have learned the euclidean algorithm now,(not the extended one)
Hi;
So the first solution can only be achieved by guessing?
Hi;
Could you explain it further(i don't know the Euclidean algorithm) 