-
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: December 2013
Puzzle | Num3er 2014
Older post: Puzzle | Num3ers 2013 and 2014 2014 has 8 divisors: 1 2 19 38 53 106 1007 2014 Sum of divisors: 3240 2013, … Continue reading
Puzzle: X in base 8 and Y in base 9
X is a 4-digit number in base 8 Y is a 4-digit number in base 9 such as Y base-9 – X base-8 = 1 DigitSum(Y) – DigitSum(X) = 1 Find X and Y For example, 3056 … Continue reading
Num3er 371
Tweet: 371 years ago today, the great Isaac Newton was born via @CoolR1a @grahamfarmelo Newton, Sir Isaac (1642–1727) —————————————— 371 has 4 divisors: 1 7 53 371 Sum of divisors: … Continue reading
Puzzle| Sequence of repdigits: as simple as 1,2,3
1 (1+2+1) = 2^2 (1+2+3+2+1) = 3^2 (1+2+3+4+3+2+1) = 4^2 (1+2+3+4+5+4+3+2+1) = 5^2 (1+2+3+4+5+6+5+4+3+2+1) = 6^2 (1+2+3+4+5+6+7+6+5+4+3+2+1) = 7^2 (1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) = 8^2 (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 9^2 121 = 11^2 121*(1+2+1) = 22^2 121*(1+2+3+2+1) = 33^2 121*(1+2+3+4+3+2+1) = 44^2 121*(1+2+3+4+5+4+3+2+1) = … Continue reading
Integers such that N^5 = A^5 + B^5 + C^5 + D^5 + E^5
(1) A^5 = B^5 + C^5 + D^5 + E^5 + F^5 For example, 72^5 = 67^5 + 47^5 … Continue reading
Puzzle| Factorial of digits of prime numbers (under 1000)
2-digit primes : ab is a 2-digit prime. Conditions : Let’s find primes such that: ab > a! * b! ab – (a! * b!) ab + (a! * b!) ab * a! * b! – 1 … Continue reading
Puzzle | Num3ers 2013 and 2014
Find smallest integers (x, y) so that 2013*x is square, 2014*x a cube, and 2013*y is a cube, 2014*y a square
4-digit number abcd = (k+a)(k+b)(k+c)(k+d)
abcd = (k + a)(k + b)(k + c)(k + d) abcd is a 4-digit number and k is a positive integer. For example, k = 5 1500 = (5 + 1)(5 + 5)(5 + 0)(5 + … Continue reading
Posted in Math Beauty, Number Puzzles
Tagged 3-digit Numbers, 4-digit Num3ers, digital product, DigitProduct, Factors
2 Comments
2-digit numbers whose cube can be expressed as the sum of cubes
6^3 = 3^3 + 4^3 + 5^3 12^3 = 6^3 + 8^3 + 10^3 = 3^3 + 4^3 + 5^3 + 8^3 + 10^3 13^3 = 5^3 + 7^3 + 9^3 + 10^3 = 1^3 + 5^3 + 6^3 … Continue reading