Does anyone recognize this equation?

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SUMMARY

The equation discussed pertains to the Mobius Inversion function, specifically relating to the summation of all divisors d of k. It is confirmed that if n is a power of a prime number, the right side of the equation represents the count of monic irreducible polynomials of degree k over a finite field with n elements. This connection is explicitly detailed in the Algebraic number theory section of the Mobius inversion formula on Wikipedia.

PREREQUISITES
  • Understanding of Mobius Inversion function
  • Familiarity with divisor summation
  • Knowledge of finite fields
  • Basic concepts of algebraic number theory
NEXT STEPS
  • Research the Mobius Inversion formula in detail
  • Study the properties of monic irreducible polynomials
  • Explore the applications of finite fields in algebra
  • Learn about divisor functions and their significance in number theory
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Mathematicians, students of number theory, and anyone interested in algebraic structures and polynomial theory will benefit from this discussion.

ElliotSmith
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TL;DR
Does anyone recognize this equation? Which branch of mathematics is it?
Does anyone recognize this equation?

Which branch of mathematics is it from?
 

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It seems summation for all the divisors d of k.
 
If n is the power of a prime number, then the right side of the equation equals the number of monic irreducible polynomials of degree k over the finite field with n elements. See the section on Algebraic number theory in this Wikipedia article and the cited reference.
 

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