My Math Forum Cardinality

 Number Theory Number Theory Math Forum

 April 20th, 2017, 09:40 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 154 Thanks: 21 Cardinality How many k satisfy $\displaystyle \;$$\displaystyle 2^n -n=k^2 Example , \displaystyle 2^7 -7=11^2 \displaystyle \;$$\displaystyle n,k \in N$ Last edited by idontknow; April 20th, 2017 at 09:44 AM.
 April 20th, 2017, 11:22 AM #2 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 I can't prove it yet but it certainly looks like $(n,k)=(7,11)$ is the only integer pair such that $2^n-n=k^2$
 April 21st, 2017, 12:42 AM #3 Senior Member   Joined: Nov 2010 From: Berkeley, CA Posts: 174 Thanks: 35 Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT What about (n,k) = (1,1) or (n,k) = (0,1) [if you allow n = 0]?

 Tags cardinality

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Roli Probability and Statistics 1 June 18th, 2014 11:35 AM BenFRayfield Number Theory 0 February 15th, 2014 02:55 PM arthurduh1 Real Analysis 11 October 21st, 2010 02:21 PM Mighty Mouse Jr Algebra 8 October 19th, 2010 10:46 AM xboxlive89128 Applied Math 0 April 24th, 2010 04:39 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top