MinaHany
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 Sep 24 awarded Autobiographer Jul 10 awarded Good Question Nov 22 awarded Popular Question Jun 8 awarded Yearling Nov 11 accepted Proof using Fermat's Little Theorem Nov 11 comment Proof using Fermat's Little Theorem Ahh yes, I don't know how I didn't see it. $9n^{23}$ is congruent to $9n^3$ and so on for all the others. Thanks Harald! Nov 11 comment Proof using Fermat's Little Theorem we know that $n^{10} = 1 mod 11$ and now I'm trying to get what is $n^{23}$ and the other powers congruent to from $n^{10}$ Nov 11 asked Proof using Fermat's Little Theorem Sep 25 awarded Critic Sep 25 accepted last digit of $n^5$ and $n$ is the same digit Sep 25 comment last digit of $n^5$ and $n$ is the same digit Ahh yes that was very clear. Thank you. Sep 25 asked last digit of $n^5$ and $n$ is the same digit Aug 14 accepted Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ Aug 14 comment Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ Got it! Thank you sir. Aug 14 awarded Commentator Aug 14 comment Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ Then $2^{2k} + 5 ≡ 0 mod 3$ so $3|2^{2k}+5$ and thus $2^{2k}+5$ can't be prime and is composite. Correct? Aug 14 comment Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ I have no idea actually, I'm pretty new to mod arithmetic Aug 14 asked Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ Jun 19 awarded Self-Learner Jun 19 awarded Teacher