# 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

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## 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 * 1-digit 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

## 4-digit numbers of the form 33xx

Take all 4-digit 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 4-digit 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