In an algebra problem i may have to simplify the expression of the quotient ring :
$$(\mathbb{Z}/25\mathbb{Z})[X] / \langle 5(X+2), 2X -22, X^2 +26 \rangle $$
I know it's easy but i just can't find it, could someone explain a simple method for it?
2026-05-17 11:10:00.1779016200
A quotient of Z/25 [X]
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Polynomial division mod $25$ gives $$ X^2+26 = X^2+1 = (X+11)(X-11)+122 = (X+11)(X-11)+22 $$ Therefore $22$ in the ideal. But $22$ is a unit mod $25$ and so the ideal is the whole ring.