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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: May 2015
Diophantine equation x^2 + y^3 = z^4
Prove that the equation has no solutions for prime numbers x, y and z Find solutions where … Continue reading
3×3 Grid – 8 Triangles
All 8 triples are nondegenerate triangles, and each of the eight perimeters is 27. Find out whether this is the smallest possible solution. Is it possible to find a 3X3 grid of distinct positive real numbers … Continue reading
summagic and productmagic determinant
This is an example of summagic determinant. that is, the sum of all the elements on each row, column, and major diagonal is constant, Note that we can easily generate perfect squares and perfect cubes. … Continue reading
Diophantine equation : x^2 – 2 = y^p
Can you solve for primes
Diophantine equation x^2 – x = y^5 – y
Find all integer solutions to Do the same for the equation:
Primes Patterns – ending in digit 7
Any other examples?
Integers that can be written in base n^2 + 1with the same digits but in opposite order
Show that integers of the form and can be written in base with the same digits but in opposite order … Continue reading
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Integers aabb, Primes aab and abb
Integers of the form aabb where aab and abb are primes: Expand the list using 4digit primes, using primes of the form aaab and abbb. for example, the primes, 1117 and 1777 … Continue reading