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Algorithms and Euler's Phi Function

Prob.1 Algorithms and Euler's phi function

Let I= { 4m+10nlm, n E Z}

I= { 9m+10nlm, n E Z}

I= { 15m+51nLm, n E Z}
Use the Euclidean Algorithm. Let a>0 and b>0 be integers to find an aEZ such that I=mZ

Z=integers E=epsilon
I hope you can understand what I've written. If not let me know.

Solution Preview

1. I = { 4m+10n | m,n are in Z}
We know that the gcd(4,10) = 2. I want to find some a, b in Z, such that 4a + 10b = 2 by Euclidean Algorithm.
10 = 2*4 + 2
Then 2 = 10 - 2*4 = (-2)*4 + 1*10. ...

Solution Summary

Algorithms and Euler's Phi Function are investigated.

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