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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 non-degenerate 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
sum-magic and product-magic determinant
This is an example of sum-magic 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 4-digit primes, using primes of the form aaab and abbb. for example, the primes, 1117 and 1777 … Continue reading
Fun With Num3ers 