all the three-digit numbers for which one obtains, when dividing the number by 11, the sum of the squares of the digits of the initial number.

Question

anonymous · Answer

IMO 1960 #1
my answer is not exist, is it correct ?

phi · Answer

000 works ?

anonymous · Answer

i was using trials... let  11|abc, the quotient is xy
x^2 + y^2 that gives 3 digit number possible for (x,y) = (9,9),(9,8),(9,7),(9,6),(9,5),(8,8)(8,7),(8,6). and check one by one, get there are not number be satisfied.
that's all if im not wrong in transletting the question :D

rational · Answer

you can find solutions for all olympiad problems by simply googling

rational · Answer

see if the solutions here make sense http://artofproblemsolving.com/wiki/index.php/1960_IMO_Problems/Problem_1

anonymous · Answer

ok, thanks :D
i was missunderstanding of the question