Timeline for Integers $n$ such that $n^d + (n+1)^d$ is never prime
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2020 at 12:35 | comment | added | Max Alekseyev | @paulMonsky: Good point! Then a bettert OEIS reference is A057856, which by the way states a conjecture implying that there are no pure numbers. | |
| Sep 10, 2020 at 4:27 | comment | added | paul Monsky | The OP is allowing d to be 1, so the smallest candidate for purity, according to OEIS, is 28 | |
| Sep 9, 2020 at 22:47 | comment | added | zeraoulia rafik | You may also check the factorisation of fermat numbers | |
| Sep 9, 2020 at 22:25 | comment | added | Max Alekseyev | $n^d+(n+1)^d$ is surely composite if $d$ is not a power of 2. So, one can restrict attention to the case $d=2^k$. That is, $n$ is pure iff the corresponding generalized Fermat numbers are all composite. | |
| Sep 9, 2020 at 22:02 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |