806 Sums of consecutive squares
7.The equation(E 37 ′ )has solutions (185, 2), (2257,261), and (2849,
330). From these we construct three infinite sequences of expres-
sions of the sum of 74 consecutive squares as a square.
Answer:2252 + 226^2 +···+ 298^2 = 2257^2 ;
2942 + 295^2 +···+ 367^2 = 2849^2 ;
130962 + 13097^2 +···+ 13179^2 = 763865^2.8.The equation(E′ 44 )has solutions (242, 4) and (2222,235). From
these we obtain two infinite sequences of expressions of the sum of
88 consecutive squares as a square.1922 + 193^2 +···+ 279^2 = 2222^2 ;
59252 + 5926^2 +··· 60122 = 55990^2.