Online Course Discussion Forum

Math Challenge ll-A Number Theory

 
 
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Math Challenge ll-A Number Theory
by Neo Liang - Saturday, 15 June 2019, 8:59 PM
 

This problem is in Lecture 5. I need the solution to problem 5.23 part b.

The solution says "Modular multiplicative inverses come in pairs, where a number can be paired with itself (a number can be its own inverse)."   This solution doesn't make sense.

 
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Re: Math Challenge ll-A Number Theory
by Areteem Professor - Monday, 17 June 2019, 7:43 PM
 

This solution was missing the inverses after the remark that they come in pairs:

The inverses are:$$2 \cdot 5 \equiv 4 \cdot 7 \equiv 1 \pmod{9},$$and$$1^2 \equiv 8^2 \equiv 1 \pmod{9}.$$