Let $p,q$ be two distinct prime numbers such that $p^3 \mid q+1$. If suppose that $p \neq 2$, then can we say anything about $p,q$?
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2I reckon that $q>p$. – Angina Seng May 05 '18 at 07:43
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1What exactly are you after? I says that $q=p^3 t -1$ and $t$ must be even, e.g. $107=3^3 \cdot 4 - 1$ and by DTAP there are infinitely many such $q$, i.e. $q=p^3 (t-1) + p^3 -1$ where $\gcd(p^3, p^3 -1)=1$ – rtybase May 05 '18 at 08:01
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ok that right. thank you – Little girl May 05 '18 at 08:03