Let a and b be two numbers such that a and b - a are co-primes and b and b + a are co-primes, respectively. Which of the following is true?
a and b are co-prime
Let's consider an example. Let a = 2 and b = 3. Then b-a = 1 and b+a = 5. gcd(2,1) = 1 and gcd(3,5) = 1. So a and b-a are co-prime, and b and b+a are co-prime. Also, gcd(2,3) = 1, so a and b are co-prime. Therefore, option 4 is true.
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 ?
