1 why is gcd n n 1 1 for two consecutive integers n and, Ask an Expert

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1. Why is gcd (n, n +1) = 1 for two consecutive integers n and n+1?
2. using Fermat's theorem, find 3^201 mod 11.
3. it can be shown that if gcd (m, n) = 1 then φ(mn) = φ(m) φ(n). Using this property and the property that φ(p) = p -1 for prime, it is straightforward to determine the value of φ(n) for any n. Determine the following:

Φ(41); φ(27); φ(231); φ(440);

Calculate the following with the modulo polynomial m(x) = x8+x4+x3+x+1
03x45 27x27 34x50

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