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\(\text{Let }i\text{ be the smallest positive integer such that }3^i\equiv 5\pmod 7.\ \text{Let}\ j\ \text{be the smallest }\\ \text{positive integer such that }5^j\equiv 3\pmod 7.\text{ What is the remainder when }ij\text{ is divided by }6?\)

 May 7, 2022
 #2
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edited, original answer was in error.   Thanks Alan.

 

3^1=3

3^2=9

3^3=27

3^4=81

None above are equivalent to 5 (mod7)

 

3^5 = 243 which is equivalent to 5 (mod7)    So    i=5

 

Go through the same process to find j.   

 

What is j?    Your turn. 

 May 7, 2022
edited by Melody  May 7, 2022

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