SOLUTION: Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same.

Question 316952: Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same
:
Three consecutive odd numbers x, (x+2), (x+4); resulting 4 number digit = y
:
x^2 + (x+2)^2 + (x+4)^2 = 1000y+100y+10y+y
:
x^2 + x^2+4x+4 + x^2+8x+16 = 1111y
:
x^2 + x^2 + x^2 + 4x + 8x + 4 + 16 = 1111y
:
3x^2 + 12x + 20 = 1111y
:
y =
:
Find the value for x which gives an integer value to y (the table of a TI83 was a great help!)
x=41, y=5
:
41^2 + 43^2 + 45^2 = 5555
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