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