#1794 · Number Theory · Diophantine equations

Extremal Values of Constant

Shew that the greatest value of $c$ in order that the equation $a x + b y = c$ may have exactly $n$ solutions in positive integers is $(n + 1) ab - a - b$ , and that the least value of $c$ is $(n - 1) ab + a + b$ , zero solutions being excluded.

~20 minProof · checked by AIDiophantine equationsProof

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXVI. Indeterminate Equations of the First Degree, Examples XXVI, No. 24

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