... is enough to write 23 7 as a sum ofdistinct squares. Since 23 7 = 14 2 +5 2 +4 2 , we finally obtain1996 = 1 2 +2 2+3 2 − 4 2 − 5 2 +6 2 +···+13 2 − 14 2 +15 2 +···+19 2 . 22 . Let a, b ∈ N satisfy ... oneimmediately finds 1 = 1 2 ,2= −1 2 − 2 2− 3 2 +4 2 ,and3=−1 2 +2 2,while the case c = 0 is trivial.(b) We have a0=0andan= 1996. Since an≤ 1 2 +2 2+ ···+ n 2 =16n(n + 1)(2n +1),wegeta17≤ ... equalsQn= 120 2 n 120 /n 2 n − 1 2 =30· 120 2 (n − 1)(n− 2) ( 120 − n)n3.It is easy to check that Qntakes its maximum when n =5anda1= ··· =a5= 24 , and that this maximum equals 15 · 23 · 24 3=...