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PROJECT EULER · #0453

Lattice Quadrilaterals

Statement only · UnsolvedOriginal problem ↗

A simple quadrilateral is a polygon that has four distinct vertices, has no straight angles and does not self-intersect.

Let Q(m,n) be the number of simple quadrilaterals whose vertices are lattice points with coordinates (x,y) satisfying 0xm and 0yn.

For example, Q(2,2)=94 as can be seen below:

0453_quad.png

It can also be verified that Q(3,7)=39590, Q(12,3)=309000 and Q(123,45)=70542215894646.

Find Q(12345,6789)mod135707531.

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