
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: June 2016
Each of ab, a+n, b+n, a+b+n is a square
To find two numbers, and , whose difference, is a square and such that each, and , is a square and their sum, , is a … Continue reading
Puzzle – geometrical progression
To find 3 numbers, , in geometrical progression such that each increased by a given number is a square. … Continue reading
Integer n such sum of its aliquot divisors is a square
Some numbers never come up as aliquot sums, such as 5. They are called nonaliquot numbers or untouchable numbers https://en.wikipedia.org/wiki/Untouchable_number Let’s find the lowest such that , : … Continue reading
Sums of consecutive integers that result in a 4th power
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 … Continue reading
Puzzle #2 – Sum of aliquot divisors of a and b
Find pair of integers (a, b) with the property that the sum of the aliquot divisors of a exceeds the sum of the aliquot divisors of by a square number. Here are two examples: 99 … Continue reading
Puzzle – Sum of aliquot divisors of n
The aliquot divisors of n are the divisors of n less than n Find two squares such that if each is increased by the sum of its aliquot divisors the resulting … Continue reading
ndigit numbers whose 4th powers end with the same n digits
…………………………………………………………… …………………………………………………………… ……………………………………………………….. ……………………………………………………….. … Continue reading
ndigit numbers whose cubes end with the same n digits
1digit : = 64 = 216 = 729 2digit : = 13824 = 15625 = 117649 = 438976 3digit : = … Continue reading
When sum of reciprocal squares = 1/2
9 terms: 10 terms: 11 terms: Can you express 1/2 with less than 9 terms?
8digit numbers whose squares end with the same 8 digits
= 7588043387109376 = 166168212890625 A general form: numbers whose squares end with the same… … 2 digits: … 3 digits: … 4 digits: … 5 digits: … 6 digits: … 7 … Continue reading