The square root of 1 with mod is any number that, when squared and taken the modulus of 1, equals 1.
To prove that the square root of 1 with mod is 1, we can use the definition of the modulus function, which states that the modulus of a number is the remainder after division by that number. Since 1 divided by any number will always have a remainder of 1, the square root of 1 with mod will always be 1.
No, there cannot be any other square root of 1 with mod besides 1. This is because the modulus function only returns positive values, and the only positive number that, when squared, results in 1 is 1 itself.
The square root of 1 with mod relates to congruence in the sense that it represents all numbers that are congruent to 1 when taken the modulus of 1. In other words, any number that gives a remainder of 1 when divided by 1 can be considered a square root of 1 with mod.
Yes, the square root of 1 with mod is a unique value. As mentioned before, the only number that is congruent to 1 when taken the modulus of 1 is 1 itself. Therefore, there can only be one square root of 1 with mod, making it a unique value.