What is the difference between a % B and a modulo b?
In some calculators and computer programming languages a % b is the same as a mod b is the same as a modulo b where % or mod are used as the modulo operators. 1 mod 2 is a situation where the divisor, 2, is larger than the dividend, 1, so the remainder you get is equal to the dividend, 1.
What is the remainder of 1 mod 2 and 5 mod 10?
For 1 divided by 2, 2 goes into 1 zero times with a remainder of 1. So 1 mod 2 = 1. Similarly, 5 mod 10 = 5 since 10 divides into 5 zero times with 5 left over as the remainder. For positive numbers, whenever the divisor (modulus) is greater than the dividend, the remainder is the same as the dividend.
How to prove if a mod b b mod a?
Here we have to prove that if a mod b = b mod a, then a=b. Try to find a direct proof, and then give up and do the contrapositive: assume a ≠ b, and prove that a mod b ≠ b mod a. There are two possible cases: a < b and b < a (we’ve already assumed a≠b). Case 1: a < b Then a mod b=a.
What if a mod b increases a by a multiple of B?
"If we have A mod B and we increase A by a multiple of B, we will end up in the same spot i.e. A mod B = (A + K * B) mod B for any integer K." Perhaps going through the proof a couple times while substituting in actual numbers will help.
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Solved: Topic: Modular Arithmetic And Multiplication Prove
