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Euler's Phi Function

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(a) I= {4m+6n l m, n E Z} closest to (and including) 0.
E=epsilon Z=integers
(b)Show that the set I is closed under addition and multiplication
(c)Use part (a) to find an mEZ such that I=mZ.

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Solution Summary

Euler's Phi Function is investigated. The addition and multiplication sets are examined.

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I = { 4m+6n | m,n are in Z}
(a) By Euclidean algorithm, we have
6 = 4 + 2,
4 = 2*2
So gcd(4,6) = 2, and 2 = 6 - 4 = (-1)*4 + 1*6
Now let m ...

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