![]() ![]() 200-level courses are usually beyond the introductory level, although many 200-level courses are open to first-year students and to majors and non-majors.100-level courses are usually introductory courses some 100-level courses do have prerequisites, and students are advised to consult the description for each course. ![]() The following policy has been used in assigning primary course numbers: A course with a given three-digit primary course number can only be taken once for credit unless specifically indicated otherwise by the department. These two digits indicate that the special focus for this HIST 101 course is The History of Islam. The last two digits are the secondary course number. The next three digits are the primary course number (101 is the primary course number for all Introduction to Historial Study courses). The first letters are the department or program abbreviation. The next two digits are the secondary course number and indicate whether there is a special focus for the course. The first three digits indicate the primary course number. What is statement $1$? Maybe then I can understand why it contradicts it.The College of Wooster uses a five-digit course numbering system. Supposed $n$ is composite, it can be then written in the form $n = ab, a, b > 1 \implies (2^a)^b - 1$ is prime with $b>1$ and $2^a>2$, contradicting statement $1$. ![]() This means that $2^n - 1$ is prime if $n$ is prime.įor the last one, we have a hint "Follow the example in lectures to show that $2^n - 1$ is not divisible by $3$", but I missed this lecture and haven't had a chance to get the note, so can someone help me with the divisible by $3$ bit and then I can try the divisible by $7$ bit myself.ĮDIT: I found a simpler proof for the second bit online: Deduce that there is a prime gap of length $\geq n$ for all $n \in \mathbb)$ which is now composite and so if $n = ab$, then $2^n - 1$. ![]()
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