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Problem 1 – Prove that every natural number n, co-prime with 10, has a multiple of who consists, when written in the decimal system, entirely of the digit 1 (is a so-called repunit)
Problem 2 – Prove that the sum of all totitives of n (numbers less than n and co-prime with n) of a number n is ½* n* (n)

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The first observation we do is that if we fix a totative k for n, then n-k is also a totative. The proof is straightforward. Since k is totative => (k,n)=1. Assuming that (n-k, n) is not 1=> we assume there is d a divisor >1 for both n-k and n...

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