Problem #6

There are two related questions this month:

• Note that

  1	=	12
  2	=	-12 - 22 - 32 + 42
  3	=	-12 + 22
  4	=	-12 - 22 + 32
  5	=	12 + 22.

  Can every positive integer n be written as a₁ 1² + a₂ 2² + ... a_k k², where a_i = ±1?

  Source: Loren Larson

• What if we use cubes instead of squares?

Back to the Archives

---

Back to the Math Department Homepage.

---