3

Part of 2009 Baltic Way

Problems(1)

Choosing signs for sum of squares

Source: Baltic Way 2009

n

be a given positive integer. Show that we can choose numbers c_k\in\{\minus{}1,1\} (

i\le k\le n

) such that 0\le\sum_{k\equal{}1}^nc_k\cdot k^2\le4.

algebrapolynomialnumber theory proposednumber theory