Find all x which are equivalent to one modulo 2 3 5 7 and 11

Find all x which are equivalent to one modulo 2, 3, 5, 7, and 11.

Solution

By definition, a modulo n means the remainder of a divided by n. Example: 5 modulo 2 = 1 because if 5 is divided by 2, the remainder is 1.

If one employs the above definition of modulo, one can see the following:

1 modulo 2 = 1, because if 1 is divided by 2, the remainder is 1. (of course, quotient is 0, but that won\'t be considered in the definition of modulo; only the remainder is to be noted).

Similarly, 1 modulo 3 = 1, because if 1 is divided by 3, the remainder is 1.

Similarly, we can note that in all the numbers given: 2,3,5,7 and 11, if 1 is divided by each of the given 5 numbers, the quotient is 0 and remainder is always1 in each case. So, x = 1 is required answer.