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)
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.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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