Solve: x^3-3x^2+27 is congruent to 0 (mod 225)

ringearV 2021-01-30 Answered
Solve:
x33x2+27 is congruent to 0 (mod 225)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

likvau
Answered 2021-01-31 Author has 75 answers
Step 1
Consider the following problem x33x2+270(mod225)
Prime factorization of 225 is 32×52
Now, 225=32×52x33x2+27 implies that the polynomial is reducible over F3andF5
So, there is a solution under 3 with x=0 and a solution under modulo 5 with x=1
Since the modulus is composite , so we solve the equation with mod(32×52)
Therefore, we have
x=0(mod 3)
x=1(mod 5)
Step 2
Now, using Chinese remainder theorem for
x=0(mod 3)
x=1(mod 5)
we get x=6
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more