Question

(1 pt) Solve each of the following congruences. Make sure that the number you enter is in the range 10, M – 1 where M is the modulus of the congruence. If there is more than one solution, enter the answer as a list separated by commas. If there is no answer, enter N. (a) 38.r = 1 (mod 273) x= (b) 183.x = 123 (mod 273) x =

Answer 1

a) 38x = 1 (mod 273)

ans: x =194 ( one method to find the answer is 38x =273t +1 ,

put t=0,not possible ,then put t=1,2,3,4,5,................

continue putting values fot t ,check whether we are getting is a multiple of 38

when we put t=27, we get 38 x= (273*27)+1 =7372, which is a multiple of 38

we get x=194)

b) 183x =123 (mod 273)

ans: x = 32 ( here we take 183x = 273t +123

continue putting values fot t =1,2,3,4,.........

check whether we are getting is a multiple of 183

when we put t=21 ,we get 183x = (273*21)+123=5856 ,which is a multiple of 183

we get x = 32 )