k,a,b,c,d be positive integers

Solve the system of equations

$\displaystyle 3^k-2=abcd$

$\displaystyle 2(3^{k-1}-1)=(a-1)(b-1)(c-1)(d-1)$

or prove that no solutions exist

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- Jan 20th 2013, 03:13 AMwauwauStrange diophantine equation
k,a,b,c,d be positive integers

Solve the system of equations

$\displaystyle 3^k-2=abcd$

$\displaystyle 2(3^{k-1}-1)=(a-1)(b-1)(c-1)(d-1)$

or prove that no solutions exist - Jan 20th 2013, 03:34 AMBobPRe: Strange diophantine equation
Well, a=b=c=d=k=1 is a solution.

- Jan 20th 2013, 03:52 AMwauwauRe: Strange diophantine equation
Any other solutions beside the trivial one?