Find three consecutive odd whole numbers such that the sum of their squares is a four-digit number whose digits are all the same.
Source: mathcontest.olemiss.edu 7/16/2007
Let be an odd whole number. Then, form three consecutive odd numbers.
Sum of squares
Since is odd, is odd. If is odd, then is odd and if is odd, then is odd. So we will try different four-digit odd numbers starting from 1111, 3333, 5555, etc.
Guess and check
Not a solution because is a whole number.
Not a solution.
Answer: 41, 43, 45.