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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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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
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
Integer triangle(a,b,c); (a+b+c),(a+bc),(b+ca) and (a+cb) are all squares
See also: Pythagorean quadruple Contributors: Max Alekseyev & Paul
IntegerSided Triangles with integral medians
According to http://arxiv.org/vc/arxiv/papers/0901/0901.1857v1.pdf … in Proposition 2, we prove that each integersided triangle can have at most two medians of integer length Can you disprove this claim? That is, find an integersided triangle with all three median … Continue reading
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
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
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
Grid  Numbers from 1 to 25
Find the arrangement of the array :