TY - JOUR
AB - PROBLEMS LES REID, Editor EUGEN J. IONAS¸CU, Proposals Editor Missouri State University Columbus State University RICHARD BELSHOFF, Missouri State University; MAHYA GHANDEHARI, University of Delaware; EYVINDUR ARI PALSSON, Virginia Tech; GAIL RATCLIFF, East Carolina University; ROGELIO VALDEZ, Centro de Investigaci´on en Ciencias, UAEM, Mexico; Assistant Editors Proposals To be considered for publication, solutions should be received by November 1, 2022. 2146. Proposed by Kenneth Fogarty, Bronx Community College (emeritus), Bronx, NY. Let a and d be integers with d> 0. We say that (a, d) is good if there is an arithmetic sequence with initial term a and difference d that can be split into two sequences of consecutive terms with the same sum. In other words, there exist integers k and n with 0 <k <n such that k−1 n−1 (a + di) = (a + di) . i=0 i=k If there is no such arithmetic sequence, we say that (a, d) is bad. (a) Show that if 2a> d , then (a, d) is good. (b) Show that if 2a = d , then (a, d) is bad. (c) Show that if a = 0 (and hence 2a< d ), then (a, d) is good. (d) Show 
TI - Problems and Solutions
JO - Mathematics Magazine
DO - 10.1080/0025570X.2022.2061246
DA - 2022-05-27
UR - https://www.deepdyve.com/lp/taylor-francis/problems-and-solutions-h2RseSo6ex
SP - 242
EP - 250
VL - 95
IS - 3
DP - DeepDyve
ER -