Which integers leave a remainder of 1 when divided by 2 and

Which integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided by 3? (Prove your answer.)

Solution

Integers leave a remainder of 1 when divided by 2 are 3,5,7,9,11,13,15,17,19 ,21,23,25,27,................................

Integers leave a remainder of 1 when divided by 3 are 4,7,10,13,16,,19,.22,25,28,..........................

Integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided by 3 are

7,13,19,25,31............[These integers   leave a remainder of 1 when divided by 6]