Find $\mathbb Z/25\mathbb Z$ $ab=0.$
I really am lost on how to start the question. Can anyone throw me a bone?
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Suppose that the prime factorization of $455$ is $(p_1)^{a_1} \times \cdots \times (p_r)^{a_r}.$ If I am interpreting the question correctly, for each prime $p_i$ in ${p_1, \cdots, p_r}$, then $p_i$ must show in one or both of the prime factorizations of $x,y$ such that the prime factorization of $(x \times y)$ contains $(p_i)^{b_i} ~: ~b_i \geq a_i$. – user2661923 May 30 '21 at 23:16
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Hint: In $\mathbb Z_{12}$, solutions would be $(3,4),(2,6),(6,6),(8,9)$ among others. Do you see how to find solutions? It's all about factorisaion.
Milten
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Please strive not to add more dupe answers to dupes of FAQs, cf. site policy here. – Bill Dubuque May 30 '21 at 23:33
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@BillDubuque My mistake, thank you for pointing it out. I can't delete it now unfortunately. – Milten May 31 '21 at 00:14