Question

(m+1)² = 24n+ 2m +2. m is less than 100 and n is any whole number. Find the number of possible values of m ?

• A. 10
• B. 32
• C. 18
• D. none of these

Answer 1

The correct option is D none of these

Option (d)

m${}^2$ -1 =24n. This means that when m${}^2$ is divided by 24 it leaves a remainder -1.

m is of the form (6p+1)${}^2$ or (6p-1)${}^2$.. This is equal 12p(3p+/-1)+1..

We can see that the term 12p(3p+/-1) Is always divisible by 24..,Therefore we have to find the possible values of (6p+1) and ( 6p-1) less than 100.

Answer is 33..