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Number Theory (MA3Z7)
Problem Sheet VII
1. Show that the von Mangoldt function Λ(n) has generating function 
2. Show that for −1 < x < 1,
[Hint: you may differentiate 
term-by-term.]
Deduce that
[Hint: d(n 2 ) is multiplicative.]
3. Show that for all N ≥ 1,
and hence that 