Call-a-positive-integer-n-good-if-there-are-n-integers-positive-or-negative-and-not-necessarily-distinct-such-that-their-sum-and-product-are-both-equal-to-n-e-g-8-is-good-since-8-4-2-1-1-1-1-1-

Question Number 21784 by Tinkutara last updated on 03/Oct/17

Call a positive integer n good if there

are n integers, positive or negative, and

not necessarily distinct, such that their

sum and product are both equal to n

(e . g . 8 is good since

8 = 4 \cdot 2 \cdot 1 \cdot 1 \cdot 1 \cdot 1 (- 1) (- 1) = 4 + 2 + 1 + 1 + 1

+ 1 + (- 1) + (- 1)) .

Show that integers of the form 4 k + 1

(k ⩾ 0) and 4 l (l ⩾ 2) are good .