[Latexpage]

# Numbers

The number of persons who booked ticket for the New Year’s concert is a perfect square. If 100 more persons booked ticket then the number of spectators would be a perfect square plus 1. If still 100 more persons booked ticket then the number of spectators would be again a perfect square. How many persons booked ticket for the concert?

### Solve our previous ‘questions of the day’

1. Greater than 40.

1. Hehe ‘Greater than 1’ is also correct :p

2. Approach sir 😛

1. Sir, I meant the square root of the number of people who attended the concert will be greater than 40. This is because no squares of natural numbers below 40 fit the pattern as mentioned in the question 🙂

2. Abhishek Tandon

People who attended concert =2401

49^2,50^2,51^2

1. Abhishek Tandon

My approach:
a^2+100=b^2+1
b^2-a^2=99

b^2+101=c^2
c^2-b^2=101
(c-b)(c+b)=101
Since 101 is prime
So, factors must be prime and 1
c-b=1 means c=b+1
c+b=101 means 1+2b=101
b= 50
c=51
Hence a=49

3. 2401

4. Sumit Singh

2401

5. shivam mukherjee

2401