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Numbers and Proofs
Find the highest common factor of 3883 and 2739, and write it in the form 3883+2739b.
I worked out the HCF so (3883, 2739) = 11
It's the latter part of the question that I need help with.
Thanks in Advance.
I worked out the HCF so (3883, 2739) = 11
It's the latter part of the question that I need help with.
Thanks in Advance.
Do you know Euclid's Algorithm? That'll sort the problem out in a jiffy, so give it a wiki
Tr4pSt3R
Find the highest common factor of 3883 and 2739, and write it in the form 3883+2739b.
I worked out the HCF so (3883, 2739) = 11
It's the latter part of the question that I need help with.
Thanks in Advance.
I worked out the HCF so (3883, 2739) = 11
It's the latter part of the question that I need help with.
Thanks in Advance.
Presumably you used the Euclidean Algorithm to get to 11? If so, just 'reverse' it i.e. rewrite each line in terms of the remainder, start from the bottom and substitute all the remainders in (best if you simplify as you go).
EDIT: Also, I think you mean 3883a + 2739b.
Incidentally, how would you find other values for a and b? They are clearly not unique.
silent ninja
Incidentally, how would you find other values for a and b? They are clearly not unique.
Is this a question for the OP to think about, or something that you are unsure about?
Daniel Freedman
Is this a question for the OP to think about, or something that you are unsure about?
Something I am unsure about.
3883a + 2739b = 11
Dividing through by 11 gives 353a + 249b = 1.
The Euclidean Algorithm tells us that a = -79, b = 112 is a solution.
Let a = -79 + A, b = 112 + B. Substituting these in gives:
353(-79+A) + 249(112+B) = 1
⇒ -27887 + 353A + 27888 + 249B = 1
⇒ 353A + 249B = 0
⇒ 353A=-249B
Since 353 and 249 are coprime, it follows that an integer k exists such that A = -249k and B = 353k. Hence the solutions are a = -79 - 249k, b = 112 + 353k
Dividing through by 11 gives 353a + 249b = 1.
The Euclidean Algorithm tells us that a = -79, b = 112 is a solution.
Let a = -79 + A, b = 112 + B. Substituting these in gives:
353(-79+A) + 249(112+B) = 1
⇒ -27887 + 353A + 27888 + 249B = 1
⇒ 353A + 249B = 0
⇒ 353A=-249B
Since 353 and 249 are coprime, it follows that an integer k exists such that A = -249k and B = 353k. Hence the solutions are a = -79 - 249k, b = 112 + 353k
Daniel Freedman
3883a + 2739b = 11
Dividing through by 11 gives 353a + 249b = 1.
The Euclidean Algorithm tells us that a = -79, b = 112 is a solution.
Let a = -79 + A, b = 112 + B. Substituting these in gives:
353(-79+A) + 249(112+B) = 1
⇒ -27887 + 353A + 27888 + 249B = 1
⇒ 353A + 249B = 0
⇒ 353A=-249B
Since 353 and 249 are coprime, it follows that an integer k exists such that A = -249k and B = 353k. Hence the solutions are a = -79 - 249k, b = 112 + 353k
Dividing through by 11 gives 353a + 249b = 1.
The Euclidean Algorithm tells us that a = -79, b = 112 is a solution.
Let a = -79 + A, b = 112 + B. Substituting these in gives:
353(-79+A) + 249(112+B) = 1
⇒ -27887 + 353A + 27888 + 249B = 1
⇒ 353A + 249B = 0
⇒ 353A=-249B
Since 353 and 249 are coprime, it follows that an integer k exists such that A = -249k and B = 353k. Hence the solutions are a = -79 - 249k, b = 112 + 353k
That's neat.
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