Note on Consecutive Integers Whose Sum of Squares Is a Perfect Square

Sums of Squares of Consecutive Odd Integers

“…Recently several papers have appeared relative to the sums of squares of consecutive integers: [11, [2], [3], [4]. The obvious extension of these investigations is to sums of squares of consecutive terms in arithmetic progressions.…”

“…The common factor of the terms on the left-hand side indicates that we mnay make the substitution z=3k(3m+1)X z' and transform the equation to (4) 3x2 + 6(n -1)x + 2(n -1)(2n -1) = (3m + 1)z'2.…”