# Monthly Archives: July 2014

## Pythagorean triples with a leg that is a semiprime (semiprimes < 100)

semiprimes less than 100 : 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95 … Continue reading

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## N^2 + DigitReversal(N^2) is a semiprime

Find square numbers N^2 such that (1)   the reversal of digits of N^2 is a prime number, and (2)   the square number   N^2 + its digits reversal DigitReversal(N^2) is a semiprime     Contributors:   Paul, … Continue reading

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## Integer triangle(a,b,c); (a+b+c),(a+b-c),(b+c-a) and (a+c-b) are all squares

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## Integer-Sided Triangles with integral medians

According to http://arxiv.org/vc/arxiv/papers/0901/0901.1857v1.pdf … in Proposition 2, we prove that each integer-sided triangle can have at most two medians of integer length   Can you disprove this claim? That is, find an integer-sided triangle with all three median … Continue reading

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## Primorial puzzle

Part 1     To find   (m, n)   so that   C(m,n)   is a product of all prime numbers ≤ m For example,     It appears that the product of the primes is … Continue reading

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## when the sum of consecutive cubes is a square

Nicomachus’s Theorem http://mathworld.wolfram.com/NicomachussTheorem.html       To find a sum of four or more consecutive cubes – not starting with 1 – giving us the square of an integer     Paul found:       From Republic of … Continue reading

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## Integers (A,B); A+B, A^2 + B^2 and A^3 + B^3 are all squares

David found:

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## Equation | a^7 + b^3 = c^2, gcd(a,b,c) = 1

David Radcliffe sent me a link to “primitive solutions to x^2 + y^3 = z^7” http://arxiv.org/abs/math/0508174v1

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## Difference of two consecutive cubes

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## Grid | Numbers from 1 to 25

Find the arrangement of the array :

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