Monthly Archives: October 2012

Reducible Polynomial for every prime p

In an algebra course, whenever we are asked to prove that a certain monic polynomial is irreducible in , it is a useful to trick to reduce the coefficients of this polynomial modulo for some prime and show that the … Continue reading

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Sum of first n factorials

In my latest number theory assignment, there was a recurrence relation defined by Letting we can manipulate the recurrence relation to solve for and then solve back for . The result is that So it is pretty neat fact that … Continue reading

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Representing primes as sum of two squares

It is a famous theorem due to Fermat that every prime 1 mod 4 can be written as sum of two squares of positive integers. On the other hand, it is not possible to represent primes 3 mod 4 as … Continue reading

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