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Congruences, Equivalence Relations and Inverses

1. Show that a = b mod m is an equivalence relation on Z.
I used = to mean "equal by definition to" and Z as integers.

2. Find the inverse of each of the following integers.

r 1 2 3 4 5 6
-----------------------------------
r^-1 mod 7

3. Show that there are no integers x and y such that x^2 and Y^2 = 19.

I think with these examples I can figure out some of the others.

Solution Summary

Congruences, Equivalence Relations and Inverses are investigated. The solution is detailed and well presented.

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