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A Complete Resolution of the {0,1} Case of Guy's Problem F24

open access: yes
We prove that the only positive integers whose square contains only the digits 0 and 1 are the powers of 10. This settles the {0,1} subcase of Guy's Problem F24. The proof reduces the condition to four exponential Diophantine families. Two quadratic families are excluded by an elementary ``island'' argument.
openaire   +1 more source

Pivotal plasmids drive the global spread of CTX-M-27 in Escherichia coli. [PDF]

open access: yesInfection
Zhang Y   +11 more
europepmc   +1 more source

A deep dive into shrimp allergy: clinical spectrum of shrimp allergy in a Tunisian pilot study. [PDF]

open access: yesFront Allergy
Krir D   +10 more
europepmc   +1 more source

Enterohaemorrhagic <i>Escherichia coli</i> AdhE spirosome length correlates with enzymatic directionality and is perturbed by salicylidene acylhydrazides. [PDF]

open access: yesOpen Biol
Serrano E   +10 more
europepmc   +1 more source

Exploring Longterm Gastrostomy Use in Adults With Cystic Fibrosis. [PDF]

open access: yesPediatr Pulmonol
Loel F   +4 more
europepmc   +1 more source

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