Charlton's investigation
Level
pending
Charlton wanted to investigate a certain group of numbers that satisfy the following:
- The number is a prime.
- The number has three digits.
- The number has a digit sum of 25.
- The name can be expressed as the sum of the squares of two natural numbers.
- When the number is divided by 5, it leaves a remainder of 2
Find the largest possible number lesser than 1000
The answer is 997.
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1 solution
We have been given that it should be 3 digit number.
It should be prime.
It should leave remainder 2 when divided by 5.
This can only be done if the unit's place is 7 or 2.
We cannot take 2 because 2 at the unit's place will make the number composite by making it divisible by 2.
So we have got 7 at the unit's place.
To make the sum of the digits to be 25. We will need two more digits ranging 0 to 9.
So by trying few numbers, we get 9+9+7= 25.
So the number is 997.
Also 997=(31^2}+(6^2)