Multiples of 3 plus 1 remainder are:
3n+1
Multiples of 4 plus 1 remainder are:
4n+1
Since these multiples must be the same number must be a multiple of 12 plus a remainder of one, which is:
12n+1
And the smallest such three digit number is:
12n+1>99 subtract 1 from both sides
12n>98 divide both sides by 12
n>8.17
Since n must be an integer, n=9
So then number is 12n+1
12(9)+1=109
