Powerful number: Difference between revisions

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== References ==

* J. H. E. Cohn, A conjecture of Erdős on 3-powerful numbers, ''Math. Comp.'' '''67''' (1998), 439--440. [http://www.ams.org/mcom/1998-67-221/S0025-5718-98-00881-3/]

* {{cite journal

* P. Erdős & G. Szekeres, Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem, ''Acta Litt. Sci. Szeged'' '''7'''(1934), 95--102.

| author = Cohn, J. H. E.

* S. W. Golomb, Powerful numbers, ''Amer. Math. Monthly'' '''77'''(1970), 848--852.

| title = A conjecture of Erdős on 3-powerful numbers

* Richard Guy, Section B16 in ''Unsolved Problems in Number Theory'', Springer-Verlag, 3rd edition, 2004; ISBN 0-387-20860-7.

| journal = Math. Comp.

* D. R. Heath-Brown, Ternary quadratic forms and sums of three square-full numbers, ''Séminaire de Théorie des Nombres, Paris, 1986-7'', Birkhäuser, Boston, 1988.

| volume = 67

* D. R. Heath-Brown, Sums of three square-full numbers, in Number Theory, I(Budapest, 1987), ''Colloq. Math. Soc. János Bolyai'' '''51'''(1990), 163--171.

| year = 1998

* Wayne L. McDaniel, Representations of every integer as the difference of powerful numbers, ''Fibonacci Quart.'' '''20'''(1982), 85--87.

| pages = 439–440

* A. Nitaj, On a conjecture of Erdős on 3-powerful numbers, ''Bull. London Math. Soc.'' '''27''' (1995), 317--318.

| url = http://www.ams.org/mcom/1998-67-221/S0025-5718-98-00881-3/}}

* {{cite journal

| author = [[Paul Erdős|Erdős, Paul]] and [[George Szekeres|Szekeres, George]]

* P. Erdős| &title G.= Szekeres, ÜberÜber die Anzahl der Abelschen Gruppen gegebener Ordnung und überüber ein verwandtes zahlentheoretisches Problem, ''Acta Litt. Sci. Szeged'' '''7'''(1934), 95--102.

| journal = Acta Litt. Sci. Szeged

| volume = 7

| year = 1934

| pages = 95–102}}

* {{cite journal

| author = [[Solomon W. Golomb|Golomb, Solomon W.]]

| title = Powerful numbers

| journal = Amer. Math. Monthly

| volume = 77

| year = 1970

| pages = 848–852}}

* {{cite book

| author = [[Richard K. Guy|Guy, Richard K.]]

| pages = Section B16

* Richard Guy,| Sectiontitle B16= in ''Unsolved Problems in Number Theory'', Springer-Verlag, 3rd edition, 2004; ISBN 0-387-20860-7.

| publisher = Springer-Verlag

| year = 2004

| id = ISBN 0-387-20860-7}}

* {{cite conference

| author = [[Roger Heath-Brown|Heath-Brown, Roger]]

| title = Ternary quadratic forms and sums of three square-full numbers

| booktitle = Séminaire de Théorie des Nombres, Paris, 1986-7

| publisher = Birkhäuser

| ___location = Boston

| pages = 137–163

| year = 1988}}

* {{cite conference

| author = [[Roger Heath-Brown|Heath-Brown, Roger]]

| title = Sums of three square-full numbers

| booktitle = Number Theory, I (Budapest, 1987)

| publisher = Colloq. Math. Soc. János Bolyai, no. 51

| year = 1990

| pages = 163–171}}

* {{cite journal

| author = McDaniel, Wayne L.

* Wayne L.| McDaniel,title = Representations of every integer as the difference of powerful numbers, ''Fibonacci Quart.'' '''20'''(1982), 85--87.

| journal = Fibonacci Quart.

| volume = 20

| year = 1982

| pages = 85–87}}

* {{cite journal

| author = Nitaj, Abderrahmane

| title = On a conjecture of Erdős on 3-powerful numbers

| journal = Bull. London Math. Soc.

| volume = 27

| year = 1995

| pages = 317–318}}

== External links ==