### Exercise 14.20. Decide whether the polynomial congruence [ left(x^{3}+3 x+1right) U equiv 1left(bmod x^{4}+1right) ] is solvable in ( mathbb{R}[x] ). If it is, solve it. (Hint: Convert the congruence to an equality involving another unknown polynomial ( V ). Then proceed as you did in the previous exercise.)

Exercise 14.20. Decide whether the polynomial congruence [ left(x^{3}+3 x+1right) U equiv 1left(bmod x^{4}+1right) ] is solvable in ( mathbb{R}[x] ). If it is, solve it. (Hint: Convert the congruence to an equality involving another unknown polynomial ( V ). Then proceed as you did in the previous exercise.)