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I have this question and its a combination of the binomial theorem and nilpotent elements within a ring.

Suppose the following, a

For this question I did the following:

[tex]\sum[/tex]

If i=m, then a=0. Additionally, if i>m a=0.

That's actually as far as I've gotten.

Suppose the following, a

^{m}=b^{n}=0. Is it necessarily true that (a+b)^{m+n}is nilpotent.For this question I did the following:

[tex]\sum[/tex]

_{i=0}^{m+n}[tex]\binom{m+n}{i}[/tex]a^{m+n-i}b^{i}If i=m, then a=0. Additionally, if i>m a=0.

That's actually as far as I've gotten.

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