
Recent Posts
 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
Recent Comments
Archives
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 March 2012
 February 2012
 January 2012
Categories
Meta
Monthly Archives: August 2015
Find (x,y) so that (x+1)/y + (y+1)/x is a positive integer
You may want to prove the last statement.
Solutions to x^2 ± x*y + y^2 = z^2
Solutions to when is an odd integer Generalize this.
Open question: Positive integers as a sum of squares and cubes?
Every positive integer is a sum of four squares (Lagrange’s Theorem) It is known that every positive integer is a sum of no more than 9 positive cubes, and that every “sufficiently large” integer is a sum of … Continue reading
Puzzle  ArithmeticMean() and HarmonicMean()
Let’s take the number 10 10 has 4 divisors: 1 2 5 10 Let’s compute the Arithmetic Mean and Harmonic Mean of (1, 2, 5, 10) Multiplying the two means: … Continue reading
floor(√x – √y) = floor(√17) where (x,y) are prime numbers
Here are solutions for y = 2, 3, 5, 7
Can you find a triangular number with exactly 500 divisors?
is the smallest triangular number which has 576 divisors Can you find a triangular number with exactly 500 divisors?
Diophantine Equation x^3 + y^3 + z^3 – 3 xyz = A^3
Case #1 : , , , and , Here are the first few examples: Case #2 : , , , and , Here are the first … Continue reading
Number of divisors: d(a)=8, d(b)=18 and ba=28 (sequence:8,18,28)
Let be the number of divisors of Find positive integers such that and and the smallest pair that satisfies the two conditions are (152, 180) : 152 … Continue reading
Puzzle Digit Permutations of 123,1234,12345,123456,…
By permuting the digits of the number 123, we obtain 6 different numbers: 123, 132, 213, 231, 312, 321 The sum of these numbers is : 123 + 132 … Continue reading