MathLabs

Problem 1

Determine all three-digit numbers NN that are divisible by 1111, such that N/11N/11 equals the sum of the squares of the digits of NN.
Step 2 of 3: The condition is a simple digit computation to check per candidate
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N/11=?(digit1)2+(digit2)2+(digit3)2N/11 \overset{?}{=} (\text{digit}_1)^2+(\text{digit}_2)^2+(\text{digit}_3)^2
Detailed analysis

For each candidate N=11kN=11k (10≤k≤9010\le k\le90), compute the sum of squares of NN's three digits and compare it to k=N/11k=N/11; keep only the matches.