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Post Closed as "Not suitable for this site" by GH from MO, Max Horn, M.G., abx, Max Alekseyev
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GH from MO
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$546\cdot p+546\cdot q=1001\cdot r$

$p,q$ odd primes, r positive integer.

are there infinitely many solutions?

And what if r is a Catalan number?

$546\cdot p+546\cdot q=1001\cdot r$

$p,q$ odd primes, r positive integer.

are there infinitely many solutions?

$546\cdot p+546\cdot q=1001\cdot r$

$p,q$ odd primes, r positive integer.

are there infinitely many solutions?

And what if r is a Catalan number?

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Diophantine equation $546\cdot p+546\cdot q=1001\cdot r$

$546\cdot p+546\cdot q=1001\cdot r$

$p,q$ odd primes, r positive integer.

are there infinitely many solutions?