Solve Diophantine Equation 87x-64y=3

May 2024 ยท 3 minute read
Solve Diophantine Equation 87x-64y=3

Solve Diophantine Equation 87x-64y=3

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Enter Diophantine Equation

Solve 87x - 64y = 3 over the integers

Use Euclids Algorithm in Rewritten Form:

Calculate the GCF of (87,-64)
#Quotient1Quotient2Remainder1Remainder2RemainderFinalRewritten
187/-64-287 - (-64 x -2)87 - 128-4187 = -2 x -64 + -41-41 = 87 - -2 x -64
2-64/-411-64 - (-41 x 1)-64 - -41-23-64 = 1 x -41 + -23-23 = -64 - 1 x -41
3-41/-231-41 - (-23 x 1)-41 - -23-18-41 = 1 x -23 + -18-18 = -41 - 1 x -23
4-23/-181-23 - (-18 x 1)-23 - -18-5-23 = 1 x -18 + -5-5 = -23 - 1 x -18
5-18/-53-18 - (-5 x 3)-18 - -15-3-18 = 3 x -5 + -3-3 = -18 - 3 x -5
6-5/-31-5 - (-3 x 1)-5 - -3-2-5 = 1 x -3 + -2-2 = -5 - 1 x -3
7-3/-21-3 - (-2 x 1)-3 - -2-1-3 = 1 x -2 + -1-1 = -3 - 1 x -2
8-2/-12-2 - (-1 x 2)-2 - -20-2 = 2 x -1 + 00 = -2 - 2 x -1

GCF (87, -64) = -1

Begin rewrite of our equations:

Rearrange to solve in terms of GCF = -1

-1 = -3 - 1 x -2

Substitute our rewrite value for -2

-3 - 1(-5 - 1 x -3)
Multiply the items inside our parentheses by 1

Combine our terms for -3


-2 = -5 - 1 x -3

Substitute our rewrite value for -3

-5 - 1(-18 - 3 x -5)
Multiply the items inside our parentheses by 1

Combine our terms for -5


-3 = -18 - 3 x -5

Substitute our rewrite value for -5

-18 - 3(-23 - 1 x -18)
Multiply the items inside our parentheses by 3

Combine our terms for -18


-5 = -23 - 1 x -18

Substitute our rewrite value for -18

-23 - 1(-41 - 1 x -23)
Multiply the items inside our parentheses by 1

Combine our terms for -23


-18 = -41 - 1 x -23

Substitute our rewrite value for -23

-41 - 1(-64 - 1 x -41)
Multiply the items inside our parentheses by 1

Combine our terms for -41


-23 = -64 - 1 x -41

Substitute our rewrite value for -41

-64 - 1(87 - -2 x -64)
Multiply the items inside our parentheses by 1

Combine our terms for


-41 = 87 - -2 x -64

Substitute our rewrite value for

87 - -2()
Multiply the items inside our parentheses by -2

Combine our terms for


How does the Diophantine Equations Calculator work?

Free Diophantine Equations Calculator - Solves for ax + by = c using integer solutions if they exist
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What 1 formula is used for the Diophantine Equations Calculator?

What 4 concepts are covered in the Diophantine Equations Calculator?

diophantine equationsequationa statement declaring two mathematical expressions are equalmultiplyto add equal groups
*substitutiona simple way to solve linear equations algebraically and find the solutions of the variables.

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