Indeterminate equation a*x + b*y = gcd(a,b) (Bezout’s identity)
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When the parameter k = 0, (x0, y0) is obtained using the extended Euclidean algorithm, and the general solution is
x = x0 + k*b / gcd(a, b), y = y0 - k*a / gcd(a, b).Enter the maximum and minimum values for k as well.
When a and b are relatively prime,
the calculation becomes a*x + b*y = 1.
x = x0 + k*b / gcd(a, b), y = y0 - k*a / gcd(a, b).Enter the maximum and minimum values for k as well.
When a and b are relatively prime,
the calculation becomes a*x + b*y = 1.
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The problem required finding the solutions to the equations 5^4*x - 2^4*y = 1, 5^5*x - 2^5*y = 1, and 11^5*x - 2^5*y = 1.
In general, the solutions to a*x + b*y = gcd(a, b) are known as Bézout’s identities. We are to find these values of x and y.