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The general solution of the linear Diophantine equations
23591 The Linear Diophantine Equation Find the general solution ( if solution exist) of each of the following linear Diophantine equations:
(a) 2x + 3y = 4 (d) 23x + 29y = 25
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Solutions of Linear Diophantine Equation ax + by = c
23557 Two different forms of solutions of Linear Diophantine Equation ax + by = c
If (xo,yo) is a solution of the Linear Diophantine equation ax + by = c , then the set of solutions of the equation consists of all integer pairs
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Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields
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the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields
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Diophantine equation
224688 Diophantine Equation Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N.
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Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields
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Proofs, Diophantine equations, and sequences
equation:
169x-65y = 91
8- Find all the nonnegative interger solutions to the following Diophantine equation:
12x + 57y = 423
9- Show that the Diophantine equation ax2 + by2 = c does not have any integer solutions
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Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.
50267 Euclidean algorithm, primes and unique factorization, congruence Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial
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Diophantine equation
26408 A proof and a solution involving a Diophantine equation Show that the Diophantine equation x^2-y^2=n is solvable in integers if and only if n is odd or n is divisible by 4. When this equation is solvable, find all integer solutions.