Let $r_n=11..11$ be the repunit of 1 repeated n times. In base 10, we have $r_n= (11..11)_{10}=\frac 19 (10^n-1)$ with a repetition of 1 n times. I would like to prove that if n is composite, then $r_n$ is also composite. I know that this question is addressed on this site, but I want to know if the following reasoning is correct. In base 2, $(11..11)_2= 2^n -1$. However, $M_n=2^n-1$ is a Mersenne number, and it is known that among the properties of Mersenne numbers, if n is composite, then $M_n$ is composite. Therefore, if n is composite, we conclude that $(11..11)_2$ is composite. Question Is it sufficient to say that $r_n=(11..11)_{10}$ is also composite?
2026-02-23 04:50:16.1771822216
About repunit and Mersenne numbers
32 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MERSENNE-NUMBERS
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