Monthly Archives: October 2013

Prime factorization of Num3ers from 4 to 1000

4 = 2 * 2 6 = 2 * 3 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 12 = 2 * 2 * 3 14 = 2 * 7 15 … Continue reading

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Concatenation| Num3ers ABCDE such that ABCDE = 45*A*B*C*D*E

    5-digit number: A,   B,   C,   D,   E   are all 1-digit numbers. 77175   =   45   *   7   *   7   *   1   *   7   … Continue reading

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System of equations | (x + y)^n = z, n= 3,5

  To find all possible triplets (x, y, z) of real numbers with x ≤ y ≤ z that                                           (1)                                   (x + y)^3   =   z                                   (y + z)^3   =   x                                   (z … Continue reading

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Composite Num3ers and their Prime factors w/ same digits

  Number  1255 Property:      the number and its prime factors have the same digits: 1255  =  5  *  251   12955   =   5   *   2591 1299955   =   5   *   259991 … Continue reading

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Integers under 1000 expressible as a sum of four integer cubes

  All integers  n ≤ 350 can be expressed as a sum of four cubes for example,   2   =   (-22)^3   +   4^3   +   (-41)^3   +   43^3 30  =  4^3  +  (-5)^3 … Continue reading

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Num3er 1024

  October 24  can be expressed as  10/24  or   1024  =  2^10 1024 = 32^2  …   It is the smallest 4-digit square number 1024  is an even square:                     … Continue reading

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DigitReversal(N), DigitSum(N) | Squares of 1202, 2012, 2021, 2022, 2102, 2202

  The squares of : 1202,   2012,   2021,   2022,   2102,   2202   1202^2  =  1444804                                         … Continue reading

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Puzzle | (x + y + z)^k – (x^k + y^k + z^k)

  (x + y + z)^2  –  (x^2  +  y^2  +  z^2)   =   2(xy  +  xz +  yz)   (x + y + z)^3  –  (x^3 + y^3 + z^3)  =  3(x + y) (x + z) (y … Continue reading

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DigitReversal(N), DigitSum(N) | Squares of 1212, 12112, 121112, …

  1212^2  =  1468944                                                                    4498641  =  2121^2 … Continue reading

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DigitReversal(N), DigitSum(N) | Squares of 1122, 11222, 112222, …

  1122^2  =  1258884                                                                        4888521 … Continue reading

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