1. Show that if n is a composite number then n divides (n-1)!
2. Find the last two digits of the number 5^5^10000.
3. Is log_10 2 rational or irrational?
4. How many zeros are there at the end of 100!
5. Can the number 111111111....1 (a string of n ones, where n >1) be a perfect square?
1. Is false for n=4. 3! = 6, and 4 does not divide 6. One thing does come to mind though, and that is if n is composite and the highest power of each prime factor is 1, it has to be true. due the factorization of (n-1)!
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