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Ex 6: We can solve the equation 3 · x + 6 ≡ 8(mod 10) by using the sum (3) and multiplication (4) rules along with the above table: 3·x+6 ≡ 8(mod 10) =⇒
13 Σεπ 2015 · Practice Problem Solutions 1. Given that 5x 6 (mod 8), nd x. [Solution: 6] 2. Find the last digit of 7100 [Solution: 1] 7100 (72) 50 49 ( 1)50 1 mod 10. 3. (1992 AHSME 17) The two-digit integers form 19 to 92 are written consecutively to form the large integer N = 192021 909192. Suppose that 3k is the highest power of 3 that is a factor of N ...
24 Μαΐ 2024 · Modular arithmetic, also known as clock arithmetic, deals with finding the remainder when one number is divided by another number. It involves taking the modulus (in short, ‘mod’) of the number used for division. If ‘A’ and ‘B’ are two integers such that ‘A’ is divided by ‘B,’ then:
Two numbers, a and b, are said to be congruent modulo n when their difference a - b is integrally divisible by n (so (a - b) is a multiple of n). Mathematically, the modulo congruence formula is written as: a ≡ b (mod n), and n is called the modulus of a congruence.
Example 1. Find x such that 3x 7 (mod 10) Solution. Based on our previous work, we know that 3 has a multiplicative inverse modulo 10, namely 3'(10) 1. Moreover, '(10) = 4, so the inverse of 3 modulo 10 is 33 Hence, multiplying both sides of the above equation by 7, we obtain. 3x 7 (mod 10) , 7 3x 7 7 (mod 10) , x 49 9 (mod 10)
1 Φεβ 2021 · How To Do Modular Arithmetic. This means that modular arithmetic finds the remainder of a number upon division! Example #1. What is 16 mod 12? Well 16 divided by 12 equals 1 remainder 4. So the answer is 4! Example #2. What about 15 mod 2? Here, 15 divided by 2 equals 7 remainder 1, so the solution is 1! Example #3. And if you have 18 mod 9?
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