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You are not logged in. #1 20121020 02:28:00
EquationIs there a method for solving the equation ax+by=c where a,b,c are constants and x,y are integers #2 20121020 02:37:57
Re: EquationIf a, b and c are integers then that looks like a linear diophantine equation, and we know certain properties of that equation. For example, if c = gcd(a,b), then there are an infinite number of solutions. You can use the extended Euclidean algorithm to find those. And if we're considering gcd(a,b), then if c isn't a multiple of gcd(a,b), then that equation has no solutions. #3 20121020 02:56:19
Re: EquationCould you explain it further(i don't know the Euclidean algorithm) #4 20121020 11:31:44
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121020 12:11:15
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121020 18:43:19
Re: EquationI 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) #8 20121020 20:12:55
Re: EquationHi 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. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121021 01:36:18
Re: EquationThis back substitution is a little complex,is there any rule for which number to substitute in the steps? #10 20121021 03:44:02
Re: EquationOh,I understand it now,but what is it with the other solution method. #11 20121021 07:18:26
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20121021 11:51:32
Re: EquationI will try my best to understand those methods,so please post them. #13 20121021 12:07:32
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20121021 12:31:51
Re: EquationHi; 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. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #16 20121021 17:15:10
Re: EquationI have quite understand it,30 minutes ago I searched in wikihow and found a similar way. #17 20121021 17:23:21
Re: EquationHi Johnathon bresly; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 