(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X = {x: x=4n+1, n[tex]\in[/tex][tex]N[/tex]}

Y = {y: y=m[tex]^{2}[/tex]+m+1, m[tex]\in[/tex][tex]N[/tex]}

Find: Y[tex]\cap[/tex]X

3. The attempt at a solution

First I tried to set x=y

[tex]\Rightarrow[/tex] n[tex]^{2}[/tex]+n+1=4n+1

[tex]\Rightarrow[/tex] n[tex]^{2}[/tex]-3n=0

[tex]\Rightarrow[/tex] n(n-3)=0

[tex]\Rightarrow[/tex] n=0,3

Subbing this in to either equation yields {1,13}.

I thought I was doing okay.

However I was comparing assignments with a classmate and she had this massive set that just keeps on going: {1, 13, 21, 57, 73, 133, 157, 241, 273, ...}

After I thought about it, this made sense, as my solution only found the elements that are in both sets when n is the same for both equations, but set equality relies only on its elements, not at what stage they were reached.

She'd done this the long way round, scripting a little program to calculate all elements for both sets then compare the elements and find the common ones.

What I'd like to know is, how can I go about solving this algebraically?

Thanks in advance,

Yorick.

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# Homework Help: Finding unions of sets

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