A positive integer is said to be prime if it is not divisible by any positive integer other than itself and one. Let K be a prime number strictly greater than 5. When K2+19 is divided by 12, the remainder will be:
8
Let K be a prime number greater than 5. Then K can be written in the form 6n+1 or 6n+5 for some integer n. Case 1: K = 6n+1 K2 + 19 = (6n+1)2 + 19 = 36n2 + 12n + 1 + 19 = 36n2 + 12n + 20 When divided by 12, the remainder is 8. Case 2: K = 6n+5 K2 + 19 = (6n+5)2 + 19 = 36n2 + 60n + 25 + 19 = 36n2 + 60n + 44 When divided by 12, the remainder is 8. In both cases, the remainder is 8.
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
