# Diophantine equations whose coefficients are raising series of integers

I required (for my study) to address a Diophantine formula, specifically, $$2 a + 3 b + 4 c + 5 d = 12 .$$ And also I can conveniently address it (as an example, on remedy is $a=2, b=1, c=0, d=1$). Yet this made me ask yourself if such formulas, with their coefficients raising series of all-natural numbers, are a grandfather clause of Diophantine equations that are constantly clearly understandable, regardless of the adverse remedy to Hilbert's 10th trouble.

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2019-05-04 17:34:11
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Linear Diophantine equations are constantly understandable decidable (in straight time). If the coefficients are $a_1, a_2, ... a_n$ after that the numbers that can show up on the RHS are specifically the multiples of $\text{gcd}(a_1, ... a_n)$, and also one can locate remedies making use of the expanded Euclidean algorithm.