NOTES ON SUMS OF SQUARES OF CONSECUTIVE ODD INTEGERS,

In the latest of a series of papers, Brother U. Alfred has investigated the conditions under which the sum of the squares of N consecutive odd integers can be a square. He derives several theorems to eliminate many values of N, and finds solutions for other values. Eight numbers below 1000 193, 564, 577, 601, 673, 724, 772, 913 remain unresolved. Also, in his table of solutions there are 17 values for which the solution exceeds 10 digits, and one contains 34 digits. In this note the eight cases will be resolved, and solutions will be presented for the 17 cases, only one of which contains as many as 7 digits. A systematic procedure for finding these solutions will be demonstrated.