Monthly Archives: October 2014

Puzzle | Almost Repdigit – Divisibility

Can you find (a, b) such that each of the “almost” 6-digit numbers abbbbb,   babbbb,   bbabbb,   bbbabb,   bbbbab   and   bbbbba   is divisible by the same 1-digit number   and baaaaa,   abaaaa, … Continue reading

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Sets of primitive pythagorean triples with perimeter almost equal

(a, b, c)   is a Pythagorean and primitive with a perimeter   p (x, y, z)   is a Pythagorean and primitive with perimeter   p + 2     Find two triples     and     … Continue reading

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Heron triangle such that the Area is a square number

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Pythagorean triples – Perimeter is a perfect square

Here are some examples     Find more examples.

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Puzzle | Two rectangles

Area of rectangle #1   =   3   *   Area of rectangle #2 Perimeter of rectangle #2   =   3   *   Perimeter of rectangle #1   Here are some solutions:         … Continue reading

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A^n + A^m contain all digits from 0 to 9

To find integer   A   such that contain all digits from   0   to   9   For example       Find other examples.

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Puzzle | Two 2-digit semiprimes

Find two 2-digit numbers (A, B) such that   A,   B,   (A-B)   are all semiprimes, where the 6 primes used are all different. And   A + B   is a square     E.g.   … Continue reading

Pythagorean triples – shortest leg is prime

All the prime numbers less than 1000: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, … Continue reading

Expressing integers using only digit 1

Let F(N) be the minimum of digit 1 to represent N and using the operations (+, *)   (1) ……………… ………………   (2) Show that     (3)   Representing prime numbers Is it true for a prime … Continue reading

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Square numbers with two different digits

Can you find other examples?