- Strings of Consecutive Happy Numbers 23 Feb 2008
- solving naive r a^x2 + r a^x1 = s b^y1 + s b^y2 23 Nov 2009
- The generalized Pillai equation rax Reese Scott
- = c and related three term exponential Diophantine equations with prime bases short running title: Prime Base Exponential Diophantine Equations
- Christmas 2009 Dear Friends,
- r a^x +/-s b^y = c showing no triple solutions via bootstrapping the double solution equation r a^x0 (a^x + pma) = s b^y0 (b^y + pmb) , showing x
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Dear Gerry, We would like to submit a reworded version of the WCNT problem 007:03 we submitted
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (19) case
- The generalized Pillai equation rax Reese Scott
- Dear Gerry, I am sorry I cannot attend the West Coast Number Theory Conference this year. Reese Scott had
- Strings of Consecutive Happy Numbers 23 Feb 2008
- revised June 15, 2006 Title: Theorem 6 when a is composite
- On the generalized Pillai equation ax revised 26 June 2009
- The generalized Pillai equation rax Reese Scott
- Handling a large bound for a problem on the generalized Pillai equation Reese Scott
- This contains modules to be used for bootstrapping. We assume here that x3 >= 2 since we always have 0 = x1 < x2 < x3, and we assume y3 >= 1.
- # module for the LLL procedure. 7 Dec 2010 17 Dec 2010 with IntegerRelations ; with LinearAlgebra ;
- Showing the infinite family of three solutions (63) does not have a fourth solution via algebraic mod b b=a^d +(-1)^v
- +/-r a^x +/-s b^y = c goal: to show no more cases of four solutions. Lemma 7 case
- r a^x +/-s b^y = c showing no more than three solutions Eqn (21) bootstrapping for b <1000
- +/-r a^x +/-s b^y = c goal: to show no more cases of four solutions. Eqn (21) case with b>1000
- Sketch for Theorem 6 with a composite revised 3 Jan 2008, 5Jan 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Strings of "Consecutive" Cubic Happy Numbers 23 Feb 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Elementary treatment of pa MSC: 11D61, 11D99
- Strings of Consecutive Happy Numbers 23 Feb 2008
- r a^x +/-s b^y = c showing no more than three solutions Eqn (19) bootstrapping to show no solutions up to the fourth root or better, so a>20000 is plenty.
- Dear friends, Christmas 2006 Merry Christmas and a Happy New Year to you and your loved ones!
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (19) case
- r a^x +/-s b^y = c showing no triple solutions via bootstrapping the double solution equation r a^x0 (a^x + pma) = s b^y0 (b^y + pmb) , showing x
- Strings of "Consecutive" Cubic Happy Numbers 23 Feb 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Strings of Consecutive Happy Numbers 23 Feb 2008
- Showing the infinite family of three solutions (63) does not have a fourth solution via algebraic mod b b=a^d +(-1)^v
- Best d Value of El-Sedy and Siksek for Consecutive Happy Numbers Note that Dr. Grundman uses S_2 but we will simply use S in the explanation, which in our program is
- Smallest examples of strings of consecutive happy numbers
- Villanovans for Life Symposium Sept 30, 2010 The most famous mathematics textbook of all time, Euclid's Elements, begins with five fundamental axioms and a list of
- Showing the infinite family of three solutions in case (20) does not have a fourth solution via algebraic mod b arguments.
- Fourth Paper We find bounds on the sigma_b(a) term for all $b < 10^3$.
- r a^x +/-s b^y = c showing no more than three solutions Eqn (20) is not symmetric, and here we onluy consider a < 20000.
- Comments on Le Maohua's 1999 paper in the Proc. Japan Acad. revised 26 July 2006
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (21) case, y2=0
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (19) case
- Handling a large bound for a problem on the generalized Pillai equation Reese Scott
- Naive search for cases of | a^x -b^y | =c where one solution has x=0 or y=0. In particular, we will look only for solutions with
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (21) case, y2=0
- The equation |px | = c in nonnegative x, y.
- r a^x +/-s b^y = c showing no more than three solutions Eqn (21) bootstrapping for b <1000
- r a^x +/-s b^y = c showing no more than three solutions Eqn (20) in old paper, eqn (5) in new paper.
- +/-r a^x +/-s b^y = c goal: to find all cases of three solutions. Eqn (21) case
- naive search of \pm a^x1 \pm a^x2 = \pm b^y1 \pm b^y2 for a
- Handling a large bound for a problem on the generalized Pillai equation Reese Scott
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (21) case, y2=0
- # module for the LLL procedure. 7 Dec 2010 17 Dec 2010 11 Nov 2011 5 Dec 2011 with IntegerRelations ; with LinearAlgebra ;
- y Christmas an premature (27
- y Christmas an has been a yea
- r a^x +/-s b^y = c showing no more than three solutions Eqn (20) in old paper, eqn (5) in new paper.
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (21) case, y2=0
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (19) case
- r a^x +/-s b^y = c showing no more than three solutions Eqn (19) bootstrapping to show no solutions up to the fourth root or better, so a>170000 is plenty.
- r a^x +/-s b^y = c looking for cases of three solutions Eqn (21) case, y2=0
- The equation |px | = c in nonnegative x, y.