Congruences, Equivalence Relations and Inverses
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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.
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Congruences, Equivalence Relations and Inverses are investigated. The solution is detailed and well presented.
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1. Show that a = b mod m is an equivalence relation on Z.
I used = to ...
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