3 integers form an arithmetic progression with d=2 i.e. a, a+2, a+4.
The sum of their squares is a 4digit number divisible by 1111.
List
all
possible triplets.
The sum of the 3 squares has to be 1111, 2222, 3333, ..., or 9999.
If x is the central of the 3 numbers, then
x^2 + (x2)^2 + (x+2)^2 = N, where N is one of the 9 numbers above.
3x^2 + 8 = N, so mod(N,3) = 2; so N can only be:
2222, or 5555, or 8888
Dividing by 3 and taking the square root to get an approximation of x leads to the following triplet.
(41, 43, 45)

Posted by Larry
on 20111226 11:32:42 