The Mobius Inversion Formula
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Theory of Numbers
Mobius Theorem
The Mobius Inversion Formula
1) Prove that ∑ μ(d) φ(d) = Π (2 - p)
d/n p/n
Primitive roots modulo p
2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15.
Prime Numbers
3) The Fermat numbers are numbers of the form 2^(2^n) + 1 = φn .
Prove that if n < m, then φn| φm - 2
4) Prove that if n ≠ m, then gcd (φn, φm) = 1
5) Use the above exercise to give a proof that there exist infinitely many primes.
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Solution Summary
This solution is comprised of a detailed explanation of the Mobius Inversion Formula,
Primitive roots modulo p and Fermat numbers.
It contains step-by-step explanation for the following problem:
The Mobius Inversion Formula
1) Prove that ∑ μ(d) φ(d) = Π (2 - p)
d/n p/n
Primitive roots modulo p
2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15.
Prime Numbers
3) The Fermat numbers are numbers of the form 2^(2^n) + 1 = φn .
Prove that if n < m, then φn| φm - 2
4) Prove that if n ≠ m, then gcd (φn, φm) = 1
5) Use the above exercise to give a proof that there exist infinitely many primes.
Solution contains detailed step-by-step explanation.
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Theory of Numbers
Mobius Theorem
The ...
Education
- BSc, Manipur University
- MSc, Kanpur University
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