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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: September 2012
Consecutive numbers each divisible by a cube
(1) Two consecutive numbers each divisible by a cube. (2) Three consecutive numbers each divisible by a cube. (3) the smallest set of numbers of 4, 5, 6, 7 consecutive numbers each divisible by a cube. (1) 80 … Continue reading
Curious properties of 11, 111, 1111, …
Older post: Series of Num3ers 1111… 11 is a prime number. 111 = 3 * 37 1111 = 11 * 101 11111 = 41 * 271 ….. 1111111111111111111 (19 digits) is a prime number. … Continue reading
Squares with the same digits
A study of square numbers up to 10^5 has revealed that … … there is only one set of six squares that have the same digits: 103^2 = 10609 130^2 = 16900 140^2 = 19600 … Continue reading
Integer with 12 and 16 representations as a sum of 2 squares
160225 has 12 representations as a sum of 2 squares: It is also the smallest number that can be written as sum of two perfect squares in 12 ways. 160225 = = 15^2 + 400^2 = … Continue reading
Integer with 2 representations as a sum of 2 positive 4th powers
That is to say, N = a^4 + b^4 = c^4 + d^4 where N, a, b, c, and d are all different, nonzero, positive integers This is a problem … Continue reading
Letter sums Part 1
Letters represent numbers 0 – 9. Add horizontally and add vertically HCA + ZAA = BKZ CCL + CAK = HRC ___________________ … Continue reading
Squares where all digits are incremented by 1
Adding 1 to each of their digits means thus obtaining the repunits 1, 11, 1111, 11111, 1111111, …
3 Amazing 12digit numbers
100307124369, 111824028801, 433800063225 They are all square numbers: 100307124369 = 316713^2 111824028801 = 334401^2 433800063225 = 658635^2 The product is: 100307124369 * 111824028801 * 433800063225 = 69755469001138755^2 Sum of the digits: 1+0+0+3+0+7+1+2+4+3+6+9 … Continue reading
Sequential digits in Sums
Digits are in sequence (not necessarily in order) in the following sums: For example: 1 + 2 = 3 (1, 2, 3) 4 + 5 = 3^2 (2, 3, 4, … Continue reading
Sums using digits 1 to 9 only once
All digits 19 are used once in each sum: 173 + 286 = 459 173 + 295 = 468 127 + 359 = 486 127 … Continue reading