List all whole numbers x in the interval 1 lessthanorequalto

List all whole numbers x in the interval 1 lessthanorequalto x lessthanorequalto 100 that satisfy: x 11 (mod23)

Solution

x=11 mod 23 means

x=23m+11 ,where m is an integer

We need 23m+11>=1

23m>=-10

m>=-10/23

Hence, m>=0 since m is an integer. So smallest value m can take is m=0

23m+11<=100

23m<=89

Hence, m<=3

So values x can take are

23*0+11=11

23*1+11=34

23*2+11=57

23*3+11=80