On the Representation of Integers
William Y. Lee · Mathematics Magazine · 1974
Case 1. Suppose Ik Si is even. Since the lemma holds for m = k and k Si 1 ~~~~~~~~~~~~~~~~~~~~~~~1 is even, hence the expression sk + Sk1 +?s1 assumes every even integer from 1s to 0. It follows that the expression Sk+ 1 + Sk + Sk1 + ?+ s assumes every even (odd) integer from S1+j si to (Sk+?1 Si), if 1 Si is even (odd). By assumption, (Sk+11 si) is an even integer less than 1, if Sk+1 is even. If Sk+1 is odd, then (Sk+1X ks) < 1.