Calculate 4x modulo 14 for each x in the set 0 1 2 13 Us

Calculate 4x modulo 14 for each x in the set {0, 1, 2, . . . , 13}. Using this information, what are all of the mutually incongruent solutions to 4x 6(mod 14)?

Solution

x=0 4xmodulo = 0

x=1 4xmodulo = 4

x=2 4xmodulo = 8

x=3 4xmodulo = 12

x=4 4xmodulo = 2

x=5 4xmodulo = 6

x=6 4xmodulo = 10

x=7 4xmodulo = 0

x=8 4xmodulo =4

x=9 4xmodulo =8

x=10 4xmodulo = 12

x=11 4xmodulo = 2

x=12 4xmodulo = 6

x=13 4xmodulo = 10

x = 5 and 12 are mutually incongruent solutions to 4x=6(mod14). because 4(5)-6 = 14 and 14 when divided by 14 gives remainder 0 . similarily 4(12)-6= 42 and 42 when divided by 14 gives remainder 0.