Monthly Archives: March 2013

Num3er 1808010808

Repeat the string 1808010808   1560   times, and tack on a 1 the end:   The resulting 15601-digit number is prime, and because it’s a palindrome made up of the digits 1, 8, and 0, it remains prime when … Continue reading

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Find integer N ; N = √(x + a√p) – √(x – a√p)

  Find all integers   x   for which the expression   N   =   √(x + 70710678√173)   –   √(x – 70710678√173)   N   is an integer            

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Fibonacci numbers| a^2 + b^2 + c^2 + d^2 = e^2

The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, … Continue reading

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Prime num3ers under 100 | 10^p – p

2,   3,   5,   7,   11,   13,   17,   19,   23,   29,   31,   37,   41,   43,   47,   53,   59,   61,   67,   71,   … Continue reading

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Smallest integers formed by two digits and divisible by them

(1)   Select two distinct numbers   a   and   b,   from   2   to   9                                                    2   ≤   a   ≤   9                                                    2   ≤   b   ≤   9 … Continue reading

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Equation (a^a)^n = b^b

  (a^a)^n   =   b^b Let’s find solutions in positive integers. Trivial solution:    a   =   b   =   1   How many values of n are there for which the equation has no non-trivial solution? … Continue reading

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QWERTY Keyboard – Part 2

Older post:   Letters on the QWERTY keyboard   The English Alphabet has 26 letters.   In alphabetical order, they are: a   b   c   d   e   f   g   h   i   j … Continue reading

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Pandigital Smith Num3ers

Smith Num3ers:   Definition A Smith number is a composite number for which, in a given base (in base 10 by default), the sum of its digits is equal to the sum of the digits in its prime factorization.   … Continue reading

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Multiplication puzzle

Insert 4 multiplication signs inside the number sequence   234567898765432   and obtain a multiplication of 5 numbers. Find the largest product.   E.g.     2 * 3 * 4567 * 8 * 98765432   =   21650962941312 but this … Continue reading

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Cubes Part 4| Palindromic sums

Palindromic sums of cubes of consecutive integers:   Palindromic sums of cubes of 2 consecutive integers : x^3   +   (x + 1)^3 1^3  +  2^3  =  9                       … Continue reading

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