Question

Find the smallest positive integer that satisfies both of the following equations: = 3 (mod4) and = 5 (mod6)

Answer 1

x=3mod4

Means that when x is divided by 4 it gives an unknown integer and a remainder of 3.

x/4 = Z + 3/4

Z= (x-3)/4

Where Z is the integer

x=5 mod6

x/6 = Y + 5/6

Y = (x-5)/6

Where Y is the integer

Z-Y must be an integer on equal to zero

(x-3)/4 - (x-5)/6

3(x-3)/12 - 2(x-5)/12

(3x-9-2x+10)/12

(x+1)/12

If it is equal to 0

x=-1. But x should be positive

If it is equal to 1

x=11

Hence the smallest possible number is 11