# 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

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## (1^2+2^2+3^2+…+n^2) + (1+2+3+…+n)

or

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## 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

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## 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

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## Diophantine equation : x^2 – 2 = y^p

Can you solve                                     for primes

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## Diophantine equation x^2 – x = y^5 – y

Find all integer solutions to     Do the same for the equation:

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## (x1/y1)^n = (a1 x1^n + a2 x2^n + a3 x3^n)/(a1 y1^n + a2 y2^n + a3 y3^n)

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## Primes Patterns – ending in digit 7

Any other examples?

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## 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

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