TY - JOUR
T1 - On the success of mishandling Euclid's lemma
AU - Dudek, Adrian W.
N1 - Publisher Copyright:
© THE MATHEMATICAL ASSOCIATION OF AMERICA [Monthly 123.
PY - 2016
Y1 - 2016
N2 - We examine Euclid's lemma that if p is a prime number such that p|ab, then p divides at least one of a or b. Specifically, we consider the common misapplication of this lemma to numbers that are not prime, as is often made by undergraduate students. We show that a randomly chosen implication of the form r|ab ⇒ r|a or r|b is almost surely false in a probabilistic sense, and we quantify this with a corresponding asymptotic formula.
AB - We examine Euclid's lemma that if p is a prime number such that p|ab, then p divides at least one of a or b. Specifically, we consider the common misapplication of this lemma to numbers that are not prime, as is often made by undergraduate students. We show that a randomly chosen implication of the form r|ab ⇒ r|a or r|b is almost surely false in a probabilistic sense, and we quantify this with a corresponding asymptotic formula.
UR - http://www.scopus.com/inward/record.url?scp=84994079440&partnerID=8YFLogxK
U2 - 10.4169/amer.math.monthly.123.9.924
DO - 10.4169/amer.math.monthly.123.9.924
M3 - Article
SN - 0002-9890
VL - 123
SP - 924
EP - 927
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 9
ER -