5
$\begingroup$

I am solving a problem and the original problem is equivalent to proving that there are no positive integers $p,q$ such that $32p^7-q^7 = \pm 1$.

$\endgroup$
4
  • 1
    $\begingroup$ Observation: $q\equiv\pm1\pmod{32}$ $\endgroup$
    – Kenta S
    Oct 21, 2020 at 3:04
  • 4
    $\begingroup$ Please mention the original problem as well, so that if possible we could suggest a way of solving it without solving this question, which could even be harder than the earlier one. $\endgroup$ Oct 21, 2020 at 3:57
  • $\begingroup$ @TeresaLisbon It's a special case of Mihailescu's theorem. It's not hard to find the original problem. $\endgroup$
    – Adola
    Oct 21, 2020 at 4:08
  • $\begingroup$ just consider mod $29$ $\endgroup$
    – yisishoujo
    Oct 21, 2020 at 12:43

0

You must log in to answer this question.

Browse other questions tagged .