Let i be the smallest positive integer such that 3i≡5(mod7). Let j be the smallest positive integer such that 5j≡3(mod7). What is the remainder when ij 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.
