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 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
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Monthly Archives: January 2013
Num3er 198
The factors of 198 are: 1 2 3 6 9 11 18 22 33 66 99 198 The prime factors are: 2 * 3 * … Continue reading
Num3ers of the form ABC = AB + C^3
You can find these numbers either by running a program, or just by solving the equation of the form: 10^n * X + Y = X + Y^3, for n > 1 568 = … Continue reading
A*AA*AAA ± B*BB*BBB = 111111
3 * 33 * 333 + 4 * 44 * 444 = 111111 6 * 66 * 666 – 5 * 55 * 555 = 111111 6*66 – 5*55 … Continue reading
Digit Sum of a^x is a
(1) Goal: To find (a, x) such that DigitSum (a^x) = a. Trivial solution: 1^2 = 1 and DigitSum (1^2) = 1 34^7 = 52523350144 and 5+2+5+2+3+3+5+0+1+4+4 = 34 43^7 … Continue reading
Repdigits 11,111, …. and 88, 888, …
(0 * 9) + 1 = 1 (1 * 9) + 2 = 11 (12 * 9) + 3 = 111 (123 * 9) + 4 … Continue reading
Repdigit = Number * 1digit number
Definition: A repdigit is a natural number composed of repeated instances of the same digit E.g. 11, 222, 333, … http://mathworld.wolfram.com/Repdigit.html 111111 = 37037 * 3 = 15873 * … Continue reading
4digit numbers of the form 33xx
Take all 4digit numbers that contain two 3s and one other pair of digits That is, numbers of the form 33xx and yy33 Use only the operations add, subtract, multiply or divide Is it always possible to … Continue reading
Divisibility of AxyB by xy
Let’s look at the divisibility of a 4digit number AxyB by the number formed by the digits in the middle of the number (xy). For example: 3317 and 3977 3317 is divisible … Continue reading
Fractions Using All Digits 1 to 9 only once
Goal: To express integers as a fraction or a mixed fraction using ALL digits 1 to 9 and whenever possible the digits 0 to 9 only once. I have posted some of the following results a long time ago. … Continue reading
Pell’s equation: N*y^2 + 1 = x^2
Goal: Find all (x, y) for N = 2, 3, 4, … , 98, 99 Two examples are given on this page http://en.wikipedia.org/wiki/Chakravala_method N = 61 and N = … Continue reading