Problem of the Week 1217
True or False. For any positive integer n, it is possible to divide the integers
If one finds the unpaired integer inelegant, one can use the integers
There are many variations obtained by using different target sets. Here are some examples. And one can treat the case of odd n in two ways (as noted above) by either including 0, or allowing one unpaired number. So the general problem has this form.
Variation 1. Call an integer n "pairable" with respect to property P if the set
Variation 2. Call an integer n "pairable" with respect to property P if the the set
Which n are pairable (using either variation) for the squares? the primes? the Fibonacci numbers?
Source: G. Hamilton, K.S. Kedlaya, and H. Picciotto, Square-sum pair partitions, College Math. Journal 46 (Sept. 2015) 264-269.